EXERCISE-1
Transverse waves are possible in solids but not in fluids. Why ?
2.
Is the velocity of vibration of the medium the same as the velocity of the wave motion ?
3.
How can one distinguish experimentally between longitudinal and transverse waves ?
4.
Why don’t we hear the effects of interference when two violins are played simultaneously ?
5.
If two waves of the same frequency difference in amplitude and are propagated in opposite directions
through a medium, will they produce standing waves ? Is energy transported? Are there any nodes ?
6.
Which parts of a curve representing a longitudinal waves show compression and which rarefaction?
E
PO
A
B
D
C
Two pulses are travelling along a string in opposite directions as shown in the figure here. If the wave
velocity is 2cms–1 and the pulses are 6cm apart, sketch the pattern after 1.5 sec. What happens to the
energy at this instant ?
UD
Y
7.
IN
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1.
6cm
Does the Doppler effect increases the intensity of a wave when its source approaches the observer ?
9.
Why does sound travel faster in solids than in gases ?
10.
Why are voices heard move clearly from a distance at dusk than during the day ?
11.
A sound wave may be consider either as a displacement wave or a pressure wave. When reflection
takes place from a rigid wall, what phase change do you expect in its displacement representation and
in its pressure representation ?
12.
Shrill sounds are carried farther. Why ?
13.
In everyday life, the Doppler effect is observed readily in sound but rarely in light. Why ?
14.
A room is filled with air and carbon dioxide. If sound now travels from the roof to the floor, would it
converge or diverge gradually ?
E
AC
M
15.
ST
8.
In the diagrams below, PQ is a reflector, and 1, 2 are the waveforms at the time t0 and t0 + t, respectively.
Find the position of the waveforms at the instant t0 + 2t in each case.
P
1
1
2
2
1
1
2
2
Q
P
Q
16.
The audibility of a man standing on the ground is more than that of a man standing at the top of a
staircase. Explain.
17.
What conclusions can be drawn from the observed red-shift of the spectrum of galaxies ?
1
Explain why sound shadows are generally not so well-defined as those of light.
19.
A man stands on the ground at a fixed distance from a siren which emits a sound of fixed amplitude.
The man hears the sound louder on a clear night than on a clear day. Explain why.
20.
The quality of a song from a loudspeaker appears to change from a distance. Why?
21.
Sometimes in a stringed instrument, a thick wire is wrapped by a thin wire. Why?
22.
All harmonics are overtones but all overtones are not harmonics. Explain.
23.
When a rubber pipe is introduced into an organ pipe, the other end being connected to the ear, where
would you hear the maximum sound ?
24.
If a string were plucked or struck at the centre, what harmonics would be absent ?
A A
N
Y
N
PO
IN
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18.
In what respects does a string differ from a rod ?
26.
When a vessel is filled under a tap, the pitch of the sound emitted gradually increases. Explain. What
difference would you expect if it were filled with a heavy liquid like mercury instead of water ?
27.
Draw diagrams showing ‘pressure nodes and antinodes’ and ‘displacement nodes and antinodes’ in
the fundamental mode and the first overtone of a closed organ pipe.
28.
What is the difference between a tone and a note ?
AC
M
E
ST
UD
25.
2
EXERCISE-2
1.
Two sound waves are respectively
y  a sin(t  kx) and y  b cos(t  kx)
(D) 3 / 4
 t x 
y  4sin     
5 9 6 
3.
A  0.04 cm
(C)
f  50 Hz .
(D)
PO
then which of the following is correct ?
  18 m
(A)
(B)
v  5 cm / s
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2.
The phase difference between the two waves is
(A)  / 2
(B)  / 4
(C) 
If the equation of a progressive wave is given by
The displacement y (in cm) produced by a simple harmonic wave is given by
y  (10 / ) sin(2000t  x /17)
The period and maximum velocity of the particle in the medium respectively will be given by :
103 s and 330 m / s
(B)
(C)
103 s and 200 m / s
(D)
2t
(B)
(2 / 5) rad
(C)
( / 3) rad
(D)
( / 2) rad .
E
ST
Three coherent waves of equal frequencies having amplitude 10mm, 4mm and 7mm respectively,
arrive at a given point with successsive phase difference of /2. The amplitude of the resulting wave
in mm is given by :
(A) 5
(B) 6
(C) 3
(D) 4
The displacement y (in cm) produced by a simple harmonic wave is given by y =(10/) sin (2000 t
– x/17). The periodic time and maximum velocity of the particles in the medium will respectively
be :
(A) 10–3 s and 330 m/s
(B) 10–4 s and 20 m/s
(C) 10–3 s and 200 m/s
(D) 10–2 s and 2000 cm/s
Equation of a wave propagating in a given direction is :
AC
M
7.
(2 / 3) rad
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(A)
6.
104 s and 330 m / s .


The equation of a wave is given by y  10sin  30    . If the displacement is 5 cm at t  0 , then


the total phase at t  7.5 s will be :
5.
104 s and 200 m / s
Y
4.
(A)
S(r, t )  A sin(t  k.r )
Where k is wave number vector having direction same as that of direction of propagation of wave.
What is equation of wave travelling in a direction making an angle ,  and  with positive x, y
and z axis ?
(A) S[( x , y, z), t ]  A sin[t  k ( x cos   y cos   z cos )]
(B) S[( x , y, z), t ]  A sin[t  k ( x cos   y cos   z cos  )]
(C) S[( x , y, z), t ]  A sin[t  k ( x cos   y cos   z cos  )]
(D) S[( x , y, z), t ]  A sin[t  k ( x cos   y cos   z cos  )]
8.
A travelling wave on a string is given by y = A sin [x+  t+ /6 ]. The displacement and velocity
3
of oscillation of a point at x = 1 cm and t = 1 s is :  = 0.56/cm,  = 12/sec, A = 7.5 cm)
(A)
12.
IN
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The shape of a wave pulse at time t = 0 is given by the function, f (x) 
incorrect statement
(A) the wave may be travelling along +ve X-axis
(B) the wave may be travelling along –ve X-axis
(C) the wave may be travelling along +ve X-axis or – ve X-axis
(D) none of these
In a sonometer wire, the tension is maintained suspending a 50.7 kg mass from the free end of the
wire. The suspended mass has a volume of 0.0075 m3. The fundamental frequency of the wire is
260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will
become (approximately) :
(A)
240 Hz
(B) 220 Hz
(C) 230 Hz
(D) 280 Hz.
A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer
are 48cm apart when the wire is in unison with a tuning fork of frequency 384. When the stone
is completely immersed in water, the length between the bridges is 40cm for re-establishing unison,
the specific gravity of the material of stone is :
482  402
(B)
482
482  402
(C)
482
482
(D)
482  402
A 4 kg block is suspended from a ceiling of an elevator through a string having a linear mass density
of 1.92 × 10–3 kg/m. Find the speed (with respect to the string ) with which a wave pulse can proceed
on the string if the elevator accelerates up at the rate of 2.0 m/s2. (g = 10 m/s2)
(A) 35 m/s
(B) 57 m/s
(C) 45 m/s
(D) 50 m/s
Out of the given waves (A), (B), (C) and (D),
E
14.
ST
482
(A)
482  402
13.
x
. Then choose
1  bx 2
PO
11.
(C)
1.76 cm, 7.5 cm s–1
(D)
7.5 cm, 75 cm s–1
A conveyor belt moves to the right with speed v = 300 m/min. A pieman puts pies on the belt at
a rate 20 per minute while walking with speed 30 m/min towards a receiver at the other end. The
frequency with which they are received by the stationary observer is :
(A) 26.64 per minute (B) 30 per minute
(C) 22.22 per minute (D) 24 per minute
Y
10.
3.75 cm, 77.94 cm s–1
(B)
UD
9.
4.6 cm, 46.5 cm s–1
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y  A sin(kx  t )
y  A cos(kx  t )
....( A)
y  A sin(t  kx)
....( B)
....(C )
y  A cos(t  kx)
....( D)
emitted by four different sources S1 , S2 , S3 and S4 respectively; perfect interference phenomena will
be observed in space under appropriate conditions when :
(A)
(C)
15.
S1 emits ( A) and S 2 ( B )
S3 emits ( B) and S 4 ( D)
S 2 emits (C ) and S 4 ( D)
S 4 emits ( B) and S3 (C ) .
A wave represented by the equation y = acos  kx - t  is superposed with another wave to form
a stationary wave such that the point x = 0 is a node. The equation for the other wave is :
(A) a sin  kx  t 
16.
(B)
(D)
(B) a cos  kx  t 
(C) a cos  kx  t 
(D) a sin  kx  t 
Find the resultant of 2 waves progressing along x-axis.
4
y1 = 3sin(3t –6x)
y2 = –4cos(3t –6x)
(A) 5 sin (3t – 6x – 37º) (B) 5 sin (3t – 6x + 53º) (C) 5 sin (3t – 6x – 53º) (D) None
18.
If at a place the speed of a sound wave of frequency 300 Hz is V, the speed of another wave of
frequency 150 Hz at the same place will be :
(A) V
(B) V/2
(C) 2V
(D) 4V.
The ends of a stretched wire of length L are fixed at x = 0 and x = L . In one experiment, the displacement
of the wire is y1  ASin (x / L) sin t and energy is E1 and in another experiment its displacement
IN
T
17.
is y 2  ASin (2x / L) sin 2t and energy is E2. Then :
(A) E2 = E1
22.
PO


The equation for stationary wave is y = 0.005 cos  62.8t  3.14 x   .Its periodic time T and wave
3

length  are :
(A) 3.14 sec, 1m
(B) 1 sec, 1 m
(C) 0.1 sec, 2 m
(D) 0.1 sec, 1 m
A string is divided into three segments, so that the segments possess fundamental frequencies in the
ratio 1 : 2 : 3. Then, the lengths of the segments are in the ratio :
(A) 6 : 3 : 2
(B) 4 : 3 : 2
(C) 4 : 2 : 1
(D) 3 : 2 : 1
Y
21.
In the equation y  4 cos( 2x / 50) sin 100 t , y represents the displacement of a particle at the distance x from the origin and at the time t. Then a node occurs at the following distance:
(A) 12.5 cm
(B) 50 cm
(C) 20 cm
(D) (100/2)
UD
20.
(C) E2 = 4E1 (D) E2 = 16 E1
If 1, 2 and 3 are the frequencies of segments of a stretched string, then the frequency of the complete
string is :
(A) 123
1 1 1
(B)    
 v1 v2 v3 
1
ST
19.
(B) E2 = 2E1
(C) v1 v2 v3
(D) [v1 v2 v3]1/3
The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given
by
y = 2 cm sin[(0.6 cm–1)x] cos[(500 s–1)t]
The length of the string is :
(A) 24.6 cm
(B) 12.5 cm
(C) 20.6 cm
(D) 15.7 cm
24.
The intensity of a plane progressive wave of frequency 1 kHz is 1010 watt/m 2 . If the density of air
is 1.3 kg/m3 and the speed of sound is equal to 330 m/s, then pressure amplitude of the wave is:
26.
(A) 3  105 N/m 2
(B)
(C)
(D)
3  10 4 N/m 2
3  10 6 N/m 2
3  10 3 N/m 2 .
A point source emits sound equally in all directions in a non-absorbing medium. Two points P and
Q are at distances of 9 m and 25 m respectively from the source. The ratio of the amplitudes of
the waves at P and Q is :
(A) 5 : 3
(B) 3 : 5
(C) 25 : 9
(D) 625 : 81
In a standing wave pattern obtained in a tube filled with iodine, due to vibrations of frequency 800
cycle/sec, the distance between eleven consecutive nodes is found to be 1 m when the temperature
of iodine vapours is 352ºC. If the temperature is 127ºC, the distance between consecutive nodes
is :
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25.
E
23.
(A)
27.
0.8 m
(B)
0.072 m
(C)
1.25 m
(D)
127
 0.1 m.
352
If at a place the speed of a sound wave of frequency 300 Hz is V, the speed of another wave of
5
frequency 150 Hz at the same place will be :
(A)
(B)
2V
(D)
4V.
(B) 327°C
(C) 927°C
(D) –123°C
Three coherent sonic sources emitting sound of single wavelength '' are placed on the x-axis at




points  –  11 6 , 0 , (0 , 0) ,  11 6 , 0 . The intensity reaching a point 0 , 5  6 from
each source has the same value I0 . Then the resultant intensity at this point due to the interference
of the three waves will be :
(A) 6 I0
(B) 7 I0
(C) 4 I0
(D) 5 I0
A source having frequency f and a detector are projected in the same vertical plane as shown in
the figure. Maximum frequency recorded by the detector during flight is (2V0  velocity of sound
in air):
PO
30.
(C)
The velocity of sound at temperature 27°C is V then velocity will be 2V at
(A) 54°C
29.
V/2
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28.
V
x
cos 40t
3
(D) none of these
ST
AC
M
E
34.
4f
3
where x and y are in centimetre and t in second. The separation between two adjacent nodes is:
(A) 6 cm
(B) 4 cm
(C) 3 cm
(D) 1.5 cm
S1 and S2 are two coherent sources of sound. OA = OB. AB = 2.7, 'when is the wave length
of sound waves. Number of points of maximum intensity as one moves around the circular path of
large radius centered at O shown in the figure will be :
(A) 12
33.
(C)
The equation of stationary wave along a stretched string is given by
y  5 sin
32.
(B) 3f
UD
31.
5f
3
Y
(A)
A
S1
O
2.7
(B) 9
B
S2
(C) 10
(D) 11
Figure here shows S1 and S2 are two equally intense coherent sources emitting radiations of wavelength 20m. The separation S1S2 is 5m and phase difference between S1 and S2 is /2. A, B and
C are three distant points of observations equidistant from the mid point of PQ. The intensity of
radiations at A, B and C will bear the ratio :
P
Q
C
(A) 2: 1: 0
(B) 1: 0: 2
(C) 1: 2: 2
(D) 1: 1: 2
S1
A
S2
B
An open pipe is suddenly closed with the result that the second overtone of the closed
pipe is found
6
to be higher in frequency by 100 Hz than the first overtone of the original pipe. The fundamental
frequency of open pipe will be :
(A)
(B)
150 Hz
(D)
200 Hz.
(C) 300 Hz
(D) 375 Hz
IN
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(B) 225 Hz
An open pipe is suddenly closed at one end with the result that the frequency of third harmonic
of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open
pipe. The fundamental frequency of the open pipe is
(A) 200 Hz
37.
(C)
A pipe of length 1 m is closed at one end. The velocity of sound in air is 300 m/s. The air column
in the pipe will not resonate for sound of frequency :
(A) 75 Hz
36.
300 Hz
(B) 300 Hz
(C) 240 Hz
(D) 480 Hz.
With a closed end organ pipe of length L, the fundamental tone has a frequency :
(A) (v/2L) and all harmonics are present
PO
35.
100 Hz
(B) (v/4L) and all harmonics are present
(C) (v/4L) and only odd harmonics are present(D) (v/4L) and only even harmonics are present
38.
The fundamental frequency of a closed pipe is 220 Hz. If 1/4th of the pipe is filled with water, the
frequency of the first overtone of the pipe now is :
(A) 220 Hz
(D) 1760 Hz
Y
A pipe open at the top end is held vertically with some of its lower portion dipped in water. At
a certain depth of immersion, the air column of length 83 m in the pipe resonates with a tuning fork
of frequency 680 Hz. The speed of sound in air is 340 m/s. The pipe is now raised up by a distance
'x' until it resonates in the "next overtone" with the same tuning fork. The value of 'x' is :
(A) 20 cm
40.
(C) 880 Hz
UD
39.
(B) 440 Hz
(B) 40 cm
(C) 50 cm
(D) 25 cm
Two vibrating tuning forks produce progressive waves given by y1  4sin  500t  and
ST
y 2  2sin  506t  . These tuning forks are held near the ear of a person. The person will hear
(A) 3 beats/s with intensity ratio between maxima and minima equal to 2
(B) 3 beats/s with intensity ratio between maxima and minima equal to 9
(C) 6 beats/s with intensity ratio between maxima and minma equal to 2
A source of frequency f gives 5 beats when sounded with source of frequency 200 Hz. The second
harmonic of source gives 10 beats when sounded with a source of frequency 420 Hz. The value of
f is
AC
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41.
E
(D) 6 beats/s with intensity ratio between maxima and minma equal to 9
(A)200 Hz
42.
(C) 205 Hz
(D) 195 Hz.
The wires X and Y of a guitar produce 4 beats per second. If the tension of Y is raised , then
the number of beats becomes 2 per second. If the frequency of X is 300, then frequency of
Y is :
(A) 296 Hz
43.
(B) 210 Hz
(B) 298 Hz
(C) 300 Hz
(D) 294 Hz
At a point, beat frequency of n Hz is observed. It means :
(A) medium particles, at that point, are vibrating with frequency n Hz.
(B) amplitude of vibrations changes simple harmonically with frequency n Hz at that point only
(C) at that point, zero intensity is observed 2n times per second
(D) none of these
7
44.
Two observers A and B start from the point O to move due east and due west respectively at time
t = 0, with the same constant speed u m/s, when a source situated at d metres due south of their
starting point O emits a continuous note of frequency n hertz. The velocity of sound is v m/s and
there is no wind. With respect to the sound received by the two observers, which of the following
statements will be true ?

by n '  n 1 

IN
T
(A) The apparent frequencies of the note as heard by the two observers will be the same and given
u2 

u 2  v2 
(B) The apparent frequency of the note as heard by A will be greater than that heard by B
PO
(C) The apparent frequency of the note as heard by A will be smaller than that heard by B
(D) The frequencies of the note as heard by the observers A and B will be the same as the real
frequency n hertz.
(B) 188 Hz
(C) 200 Hz
(D) 181 Hz.
A source of sound with frequency 256 Hz is moving with a velocity v towards a wall and an observer
is stationary between the source and the wall. When the observer is between source and the wall,
he finds that the frequency of the waves received directly from the source is x and the frequency
of the waves received after reflection from the wall is y; then:
(B) x < y
(C) x = y
(D) nothing can be predicted
E
(A) x > y
AC
M
46.
219 Hz
UD
(A)
Y
A train has just completed a U-curve in a track which is a semi-circle. The engine is at the forward
end of the semi-circular part of the track while the last carriage is at the rear end of the semi-circular
track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/s. Then the apparent
frequency as observed by a passenger in the middle of the train, when the speed of the train is
30 m/s, is:
ST
45.
8
EXERCISE-3
1.
A wave traveling along a string is described by,
y ( x, t )  0.05sin (80.0 x  3.0t ) ,
At two points S1 and S2 on a liquid surface two coherent wave sources are set in motion with
the same phase. The speed of the waves in the liquid v  0.5 ms-1, the frequency of vibration v  5
Hz and the amplitude y0  0.04 m. At a point P of the liquid surface which is at a distance x1  0.30
m from S1 and x2  0.34 m from S2 a piece of cork floats
(i) Find the displacement of the cork at t  3s .
5.
ST
UD
4.
(ii) Find the time t0 that elapses from the moment the wave sources were set in motion until the
moment that the cork passes through equilibrium position for the first time.
A sonometer wire fixed at one end has a solid mass M hanging from its other end to produce tension
in it. It is found that 70 cm length of the wire produces a certain fundamental frequency when plucked.
When the same mass M is hanging in water completely submerged in it, it is found that the length
of the wire has to be changed by 5 cm in order to produce the same fundamental frequency. Calculate
the density of the material of mass M.
A wire of uniform cross-section is stretched between two points 1 m apart. The wire is fixed at
one end and a weight of 9 kg is hung over a pulley at the other end produces fundamental frequency
of 750 Hz.
(a) What is the velocity of transverse waves propagating in the wire?
(b) If now the suspended weight is submerged in a liquid of density (5/9)th that of the weight,
what will be the velocity and frequency of the waves propagating along the wire?
A metal rod of length l = 100 cm is clamped at two points A and B as shown in figure. Distance
of each clamp from nearer end is a = 30 cm. If density and Young’s modulus of elasticity of
rod material are  = 9000 kgm–3 and Y = 144 GPa respectively, calculate minimum and next
higher frequency (in kHz) of natural longitudinal oscillations of the rod.
Y
3.
PO
2.
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in which the numerical constants are in SI units ( 0.005m, 80.0 rad m 1 , and 3.0 rad s 1 ). Calculate (a)
The amplitude, (b) The wavelength, and (c) The period and frequency of the wave. Also calculate
the displacement y of the wave at a distance x  30.0 cm and time t  20s ?
E
A
B
6.
7.
8.
AC
M
30 cm
30 cm
l = 100 cm
A heavy uniform rope of length 12m is suspended from a ceiling. The rope is given a sudden side
ways jerk at the bottom so that a pulse is created at the bottom. At the same instant a particle
is dropped from the ceiling. Find the distance from the upper end of rope where the particle will
cross the pulse?.
The fundamental frequency of a sonometer wire carrying a block of mass 1 kg and density
1.8 is 260 cycle/s. When the block is completely immersed in a liquid of density 1.2 then
what will be its new frequency
[ Put your answer in round figures, e.g if you get 230.23 then write 230 only ]
Three successive resonance frequencies for a certain string are 75, 125 and 175 Hz (a) Find the
ratios of each pair of successive resonance frequencies. (b) How can you tell that these frequencies
are for a string fixed at one end only rather than for a string fixed at both ends? (c) What is the
9
13.
14.
15.
16.
IN
T
PO
Y
12.
UD
11.
ST
10.
A source is moving along a circle x 2  y 2  R 2 with constant speed
vS 
330
6 3
m/s in clock wise direction while an observer is stationary
E
9.
fundamental frequency? (d) Which harmonics are these resonance frequencies? (e) If the speed of
transverse waves on this string is 400 m/s, find the length of the string.
A certain length l of a wire when loaded with the weight of a solid vibrates in unison with a tuning
fork. When the weight is immersed in water the length of the wire resonating with the same tuning
fork is l1; when it is immersed in a liquid the length is l2. Calculate the specific gravity of the solid
and that of the liquid.
Two wires of radii r and 2r respectively are welded together end to end. This combination is used
as a sonometer wire and is kept under tension T. The welded point is midway between the two
bridges. What would be the ratio of the number of the loops formed in the wires such that the joint
is a node when stationary vibrations are set up in the wire?
A string with a mass density of 4 × 10–3 kg/m is under a tension of 360 N and is fixed at both
ends. One of its resonance frequencies is 375 Hz. The next higher resonance frequency is 450 Hz.
(a) What is the fundamental frequency of the string?
(b) Which harmonics are the ones given?
(c) What is the length of the string?
A pipe of length 1.5 m closed at one end is filled with a gas and it resonates in its fundamental
with a tuning fork. Another pipe of the same length but open at both ends is filled with air and it
also resonates in its fundamental with the same tuning fork. Calculate the velocity of sound at 0°C
in the gas. Given that the velocity of sound in air is 360 m/s at 30°C where the experiment is performed.
A tube of a certain diameter and of length 48 cm is open at both ends. Its fundamental frequency
of resonance is found to be 320 Hz. The velocity of sound in air is 320 ms 1 . Estimate the diameter
of the tube. One end of the tube is now closed. Calculate the lowest frequency of resonance for
the tube.
The driver of a car travelling at 100 km/h towards a cliff briefly sounds the horn. Exactly one second
later he hears the echo and notes that its frequency is 840 Hz. How far from the cliff was the car
when the driver sounded the horn and what is the frequency of the horn?
A source of sonic oscillations with frequency v0 and a receiver are located on the same normal to
the wall. Both the source and the receiver are stationary and the wall recedes from source with
velocity u. Find the beat frequency registered by the receiver. The velocity of sound is equal to v.
AC
M
at point (2 R, 0) with respect to the
circle. Frequency emitted by the source is f .
centre
y
S
of
O
R
R
(a)
17.
x
Find the coordinates of source when observer records the
maximum and minimum freq.
(b)
Find the value of maximum and minimum frequency.
Take speed of sound V  330 m/s
In the figure shown a source of sound of frequency 510 Hz moves with constant
velocity vs = 20 m/s in the direction shown. The wind is blowing at a constant velocity
vw = 20 m/s towards an observer who is at rest at point B. Find the frequency (in Hz) detected
by the observer corresponding to the sound emitted by the source at initial position A.
[ Speed of sound relative to air = 330 m/s ]
10
A source of sound is moving along a circular orbit of radius 3m with an angular velocity 10rad/
sec. A sound detector located very very far away from the source is excuting linear simple harmonic
motion along the line BD with amplitude BC = CD = 6m. as shown in figure. The frequency of
IN
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18.
 
A pulse travels on a string under tension. The transverse displacement of the string from its equilibrium
position is given by u = f (x – 150t) where x is in meter and t is in seconds.
Y
19.
PO
oscillation of detector is 5  per second. The source at point A when the detector is at point B.
If the source emits a continuous sound wave of frequency 340Hz, find the maximum frequency
(in Hz) recorded by the detector. (Velocity of sound = 330 m/s)
1
y (cm) 0
-1
-10 -8
-6
UD
t=0s
-4
-2
0
-1.5
2
1.5
4
6
8
10
x(m)
ST
(a) The pulse (y) is plotted as a function of x for t = 0. Draw the pulse (in the panels given)
(i) as a function of x for t = 0.04s
(ii) as a function of t for x = 0.
(b) Find the velocity of a particle at t = 0, x = 1m
t=0.04s
E
1
y (cm) 0
-1
AC
M
-10 -8
-6
-4
-2
0
x(m)
t=0m
2
4
6
8
10
1
y (cm) 0
-1
20.
-0.10 -0.08 -0.06 -0.04 -0.02 -0.00 0.02 0.04 0.06 0.08 0.10
t(s)
A symmetrical triangular pulse of maximum height 0.4 m and total length 1m is moving in the positive
x-direction on a string on which the wave speed is 24m/s. At t = 0 the pulse is entirely located between
x = 0 and x = 1m. Draw a graph of the transverse velocity of particle of string versus time at
x = +1m.,
11
EXERCISE-4
3.
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(A)
Point B is in compression
(B)
Point C is in rarefraction
(C)
Points A, C and E are at normal pressure.
(D)
Points A and C are equally rarefracted and compressed respectively
In a stationary wave there is :
(A) no energy current but there is energy density
(B) neither energy current nor energy density
(C) energy current but no energy density
(D) both energy current and energy density
A rope of length  and mass per unit length  is suspended vertically. If mass M is suspended from the
bottom of the rope. Then time for a transverse wave to travel the rope is
(A) 

Mg
(B) 2
1
(C) 2 g [ M    M ]
v
(B)
h
8.
9.
v
(C)
h
(D)
h
h
E
A wave represented by the equation y = Acos(kx –t) is superimposed with another wave to form a
stationary wave such that the point x = 0 is a node. The equation of the other wave is :
(A) –A sin(kx –t) (B) –A cos(kx + t) (C) A sin(kx + t)
(D) A cos(kx +t)
If two waves of same frequency and same amplitude respectively, on superposition, produce a resultant disturbance of the same amplitude, the waves differ in phase by :
(A) 
(B) 2/3
(C) /3
(D) 3
A particle is subjected to two mutuallly perpendicular simple harmonic motions such that its x and y


coordinates are given by x  2 sin t and y  2 sin  t   . The path of the particle will be :
4

(A) an ellipse
(B) a straight line
(C) a parabola
(D) a circle
Two waves are passing through a region in the same direction at the same time. If the equations of
these waves are :
2
y1  a sin
( vt  x )

2
y 2  b sin [ vt  x )  x 0 ]
and

then the amplitude of the resulting wave for x0 = (/2) is
AC
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7.
v
ST
(A)
6.
1
.[ M    M ]
g
(D)
A uniform rope having some mass hangs vertically from a rigid support. A transverse wave pulse is
produced at the lower end. The speed (v) of the wave pulse varies with height (h) from the lower end
as:
v
5.

g
UD
4.
PO
2.
The figure represents the longitudinal wave travelling in
+ve x-direction . Select correct alternative.
Y
1.
(A) a  b
(B) a + b
Two harmonic waves are described by
(C)
a 2  b2
(D)
a 2  b 2  2ab cos x
12
;
y1  3 sin ( x  0.6t )cm
y 2  3 sin ( x  0.6t )cm
The three smallest values of x corresponding to antinodes are :
1 3 5
1 1 1
1 1 1
1
, ,
(B) , ,
(C) , ,
(D) 0, ,1
2 2 2
3 6 9
4 3 2
2
A composite string is made up by joining two strings of different masses per unit length  and 4.
The composite string is under uniform tension. A transverse wave pulse ;
Y = (6 mm) sin (5 t + 40 x) , where 't' is in seconds and 'x' is in metres, is sent along the lighter
string towards the joint. The joint is at x = 0. The equation of the wave pulse reflected from the
joint is :
(A) (2 mm) sin (5 t – 40 x)
(B) (4 mm) sin (40 x – 5 t)
(C) – (2 mm) sin (5 t – 40 x)
(D) (2 mm) sin (5 t – 10 x)
A wave pulse on a string has the dimension shown in figure. The wave speed is v = 1 cm/s. If point O
is a free end. The shape of wave at time t = 3 s is :
10.
PO
11.
IN
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(A)
13.
(C)
(D)
x
cos 40 t . The ratio of the magnitudes of
3
frequency and amplitude of the components whose superposition gives the above wave is
(A) 8
(B) 16
(C) 4
(D) 10
Two waves given by equation
A string vibrates according to the equation y  5sin
UD
12.
(B)
Y
(A)
15.
16.
17.
In a stationary waves that forms as a result of reflection of waves from an obstacle, the ratio of
the amplitude at an antinode to the amplitude at node is 6. Percentage of energy transmitted is :
(A) 51%
(B) 50%
(C) 49%
(D) 47%
The speed of sound wave in a mixture of 1 mole of helium and 2 moles of oxygen at 27°C is :
AC
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14.
E
ST
x
x 1


y1  a cos(2)  t   and y 2  a cos(2)  t   

 2


superimposed upon each other. The resultant wave will be:
(A)
a standing wave of maximum displacement 2a at antinode and zero at node
 3 5
,
.....
(B)
a standing wave of antinodes at x = 0, /2, ......... and nodes at x  ,
4 4 4
(C)
a progressive wave of amplitude 2a and frequency 2v.
(D)
a destructive interference will take place
(A) 4 I0
(B) I0
(C) 2I0
(D) Zero
(A) 400 m/s
(B) 600 m/s
(C) 800 m/s
(D) 1200 m/s
In the figure the intensity of waves arriving at D from two coherent sources S 1 and S2 is I0 . The
wavelength of the wave is  = 4 m . Resultant intensity at D will be :
S1
4m
D
3m
A source S emits electromagnetic waves which are detected by the detector D kept at a distance of
S2
13
d
4
from the source. The waves directly received from S and those reflected by a layer at a distance d
above the ground are found to be in phase. If the layer moves up by a distance h = 0.01d, the
interfering waves are once again in phase. The wavelength of the waves from the source is about :
h
D
(A)
0.04d
(B)
0.08d
(C)
0.02d
(D)
0.01d.
Two speakers connected to the same source of fixed frequency are placed 2m apart in a box. A sensitive
microphone placed at a distance of 4m from the midpoint along the perpendicular bisector shows maximum
response. The box is slowly rotated till the speakers are in line with the microphone. The distance between
the midpoint of the speakers and the microphone remains unchanged. Exactly 5 maximum responses are
observed in the microphone in doing this, the wavelength of the sound wave is :
(A) 0.8m
(B) 0.4m
(C) 0.2m
(D) 1.6m
Sources P and Q emit radio waves of wavelength 200 m, with the phase of emission from P ahead
of that from source Q by 90°. The distance r 1 from P to detector at A is greater than the
corresponding distance r2 by 50 m. The phase difference between the waves reaching A, is :
(A) 0
(C) /2
Two wave functions in a medium are given by y1 
ST
20.
(B) 
UD
Y
19.
S
PO
18.
d
4
IN
T
d
(D) /4
1
1
y2 
2 and
2  (2 x  3t  6) 2
2  (2 x  3t )
Where x and y are in meter and t is in second.
Statement A: There is a position where resultant displacement is always zero
E
Statement B: There is an instant at which resultant displacement is zero everywhere
(B) A is true but B is false
(C) A is false but B is true
(D) Both A and B are false
AC
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21.
(A) Both A and B are true
A metal bar clamped at its centre resonates in its fundamental mode to produce longitudinal
waves of frequencies 4 kHz. Now the clamp is moved to one end. If f1 and f2 be the frequencies
of first overtone and second overtone respectively, then :
(A) 3f2 = 5f1
22.
23.
(B) 3f1 = 5f2
(C) f2 = 2f1
(D) 2f2 = f1
A tuning fork of frequency 10 Hz is brought close to a clamped string of fundamental frequency
50 Hz
(A) It will oscillate with a frequency of 10 Hz.
(B) It may be in resonance if supported at 1/5th of its length.
(C)It will never be in resonance.
(D) It will not oscillate
The standing waves are set up in organ pipe of length  . For a particular mode of vibration the
14
pressure different between the central point and one end point of pipe is maximum. Identify the
wavelength of the mode out of the following wavelength.
(A)
27.
28.
IN
T
PO
An open organ pipe of length  is sounded together with another open organ pipe of length
 + x in their fundamental tones. Speed of sound in air is v . The beat frequency heard will be
(x <<  ):
v 2
(B)
2x
vx
(C)
2 2
v x2
(D)
2
If a source sounding a whistle with a constant frequency moves in a circle and frequencies observed by
observer O, when the source is at points A,B,C be va, vb, vc, then :
AC
M
E
31.
(D) can’t be identified
(A) 42 m
(B) 4.2 102 m
(C) 1.0 m
(D) 4.2 103 m
At a point, beat frequency of n Hz is observed. It means that :
(A) medium particles at that point are vibrating with a frequency of n Hz.
(B) amplitude of vibrations changes simple harmonically with frequency n Hz at that point only.
(C) at that point, zero intensity is observed 2n times per second
(D) none of the above
Three tuning forks are available. One fork marked A produces a 440 Hz tone. The other forks are
marked X and Y. The frequency of Y is less than the frequency of X. When forks A and X are
sounded together a beat frequency of 4 Hz is heard. For forks A and Y, the beat frequency is 7 Hz.
For forks X and Y. The beat frequency is 3 Hz.
(A) The frequency of X is 433 Hz.
(B) The frequency of Y is 447 Hz.
(C) The frequency of X is 444 Hz.
(D) The frequency of Y is 433 Hz.
Forty one tuning forks are arranged in increasing order of frequencies such that every for k gives
5 beats with the next. The last fork has frequency that is double the frequency of first fork. The
frequency of the fork is :
(A) 400 Hz
(B) 210 Hz
(C) 200 Hz
(D) 205 Hz
(A) va> vb> vc (B) va< vb< vc
30.

16
If the velocity of sound in air is 336 m/s, the maximum length of a closed pipe that would produce a
first audible sound is!
vx
(A) 4  2
29.
(C)
Y
26.
2
17
UD
25.
(B)
ST
24.
4
13
A
va
B
vc
C
vb
(C) va = vb > vc
(D) none of the above
A source of sound is moving with velocity u/2 and two observers A and B are moving with velocity 'u'
as shown. Find ratio of wavelength received by A and B. Given that velocity of sound is 10 u.
(A) 19/21
(B) 17/21
(C) 21/23
(D) 17/23
Sources P and Q emit radio waves of wavelength 200 m, with the phase of emission from P ahead of
15
that from source Q by 90°. The distance r1 from P to detector at A is greater than the corresponding
distance r2 by 50 m. The phase difference between the waves reaching at A, is :
32.
(C) /2
The equation of a wave traveling along the positive x-axis, as shown in figure at t = 0 is given by
y
1
0
-0.5
-0.1
x
PO




(A) sin  kx  t   (B) sin  kx  t  
6
6






(C) sin  t  kx   (D) sin  t  kx  
6
6


A composition string is made up by joining tow strings of different masses per unit length and 4.
The composite string is under the same tension. A transverse wave pulse : Y = (6mm) sin (5t + 40x),
where ‘t’ is in seconds and ‘x’ in meters, is sent along the lighter string towards the joint. The joint is at
x = 0. The equation of the wave pulse reflected from the joint is
UD
Y
33.
(D) /4
IN
T
(B) 
(A) 0
(A) (2mm) sin (5t – 40x)
(B) (4mm) sin (40x – 5t)
(C) –(2mm) sin (5t – 40x)
In the previous question, the percentage of power transmitted to the heavier string through the joint is
approximately
ST
34.
(A) 33%
(C) 67%
(D) 75% 1
A metallic wire of length L is fixed between two rigid supports. If the wire is cooled through a temperature
difference T (Y = young’s modulus, = density, = coefficient of linear expansion) then the frequency
of transverse vibration is proportional to

Y
(B)
Y

AC
M
(A)
36.
(B) 80%
E
35.
(D) (2mm) sin (5t – 10x)
(C)

Y
(D)

Y
Consider a function y = 10 sin2 (100t + 5z) where y, z are in cm and t is in second.
(A) the function represents a travelling, periodic wave propagation in (–z) direction with speed 20m/s.
(B) the function of the wave is 5cm
(C) the amplitude of the water is 5cm
37.
(D) the amplitude of the wave is 10cm
The period of oscillation of a point is 0.04sec. and the velocity of propagation of oscillation is 300m/
sec. The difference of phases between the oscillations of two points at distances 10 and 16m respectively
from the source of oscillations is
(A) 2
(B) 
(C) 
(D) 
16
A steel wire has a mass of 5g/m and is under tension 450N. Find the maximum average power that can
be carried by the transverse wave in the wire if the amplitude is not be exceed 20% of the wavelength.
(A) 10.8 × 104 W
40.
(D) 10.8 × 82 W
IN
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Two strings A and B with  = 2kg/m and = 8kg/m respectively are joined in series and kept on a
horizontal table with both the ends fixed. The tension in the string is 200N. If a pulse of amplitude 1cm
travels in A towards the junction, then find the amplitude of reflected and transmitted pulse.
1
4
(A) A r  cm, A t   cm
3
2
1
4
(B) A r   cm, A t  cm
3
2
4
2
(C) A r   cm, A t  cm
2
3
1
2
(D) A r   cm, A t  cm
3
3
A parabolic pulse given by equation y (in cm) = 0.3 – 0.1 (x – 5t)2 (y  0) x in meter and t in second
travelling in a uniform string. The pulse passes through a boundary beyond which its velocity becomes
2.5m/s. What will be the amplitude of pulse in this medium after transmission?
(A) 0.2 cm
41.
(C) 10.2 × 102 W
PO
39.
(B) 12.8 × 104 W
(B) 0.4 cm
(C) 1.4 cm
(D) 0.5 cm
A string fixed at both ends has consecutive standing wave modes for which the distance between
adjacent nodes are 18cm and 16 cm respectively.
Y
38.
UD
(a) What is the length of the string?
(b) If the tension is 10N and the linear mass density is 4g/m, what is the fundamental frequency?
(A) (a) 144 cm (b) 17.36 Hz
(C) (a) 141 cm (b) 18.36 Hz
(A) 0.22 V
(D) 1.22 V
(B) 85%
(C) 75%
(D) 96%
A uniform string of length L and total mass M is suspended vertically and a transverse pulse is given at
the top end of it. At the same moment a body is released from rest and falls freely from the top of the
string. How far from the bottom does the body pass the pulse.
AC
M
45.
(C) 2.10 V
In a stationary wave pattern that forms as a result of reflection of waves from an obstacle the ratio of
the amplitude at an antinode and node is = 1.5. What percentage of the energy passes across the
obstacle?
(A) 92%
44.
(B) 2.22 V
E
43.
(D) (a) 142 cm (b) 19.36 Hz
The extension in a string, obeying Hooke’s law is x. The speed of wave in the stretched string is v. If the
extension in the string is increased to 1.5x find the new the speed of wave.
ST
42.
(B) (a) 145 cm (b) 16.36 Hz
(A) L/10
(B) L/3
(C) L/9
(D) L/7
An observer starts with uniform acceleration towards the source. The apparent frequency f heard
by the observer varies with time as :
(A)
(B)
(C)
(D)
17
EXERCISE-5
1.
A transverse harmonic wave on a string is described by


y ( x, t )  3.0sin  36t  0.018 x  
4

IN
T
where x, y are in cm and t in s. The positive direction x is from left to right.
(i) Is this a travelling or a stationary wave ? If it is traveling, what are the speed and direction of its
propagation?
(ii) What are its amplitude and frequency?
(iii) What is the initial phase at the origin?
A long uniform string of mass density 0.1 kg/m is stretched with a force of 40 N. One end of the
string (x = 0) is oscillated transversely (sinusoidally) with an amplitude of 0.02 m and a period of
x direction are set up.
0
.
1
s
e
c
,
s
o
t
h
a
t
t
r
a
v
e
l
l
i
n
g
w
a
v
e
s
i
n
t
h
e
+
What is the velocity of the waves ?
(b)
What is their wavelength ?
(c)
If at the driving end (x = 0) the displacement (y) at t = 0 is 0.01 m with
Y
(a)
dy
negative ,
dt
UD
2.
PO
(iv) What is the least distance between two successive crests in the wave?
What is the equation of the travelling waves ?
3.
Three metal rods are located relative to each other as shown in figure, where L1 + L2 = L3. Values of
density and Young’s modulus for the three materials are
Y1  7 1010 Pa
ST
1  2.7  103 kg / m3
Y2  1.6  1010 Pa
3  8.8  103 kg / m 3
Y3  11 1010 Pa
E
2  11.3  103 kg / m3
4.
5.
AC
M
If L3 = 1.5m, what must the ratio L1/L2 be if a sound wave is to travel the length of rods 1 and 2 in the
same time as required to travel the length of rod 3?
A uniform rope of length L and mass m is held at one end and whirled in a horizontal circle with angular
velocity . Ignore gravity. Find the time required for a transverse wave to travel from one end of the
rope to the other.
A loop of rope is whirled at a high angular speed 5 rad/s, so that it becomes a taut circle of radius
1 m. A kink develops in the whirling rope as shown in figure. Find the tension (in newton) in the
rope if the linear mass density of the rope is 1 kg/m.

R
18
6.
A string of length 1 m fixed at one end and on the other end a block of mass M = 4 kg is suspended.
x 
 . cos(100t ) where x and y
10
 
The string is set into vibration and represented by equation y  6sin 
M
(a) Find the number of loops formed in the string .
(b) Find the maximum displacement of a point at x  5 / 3 cm
PO
(c) Calculate the maximum kinetic energy of the string
IN
T
are in cm and t is in seconds.
(d) Write down the equations of the component waves whose superposition gives the wave
Two wires of different mass densities are soldered together end to end and are then stretched under a
tension F (the tension is same in both the wires). The wave speed in the second wire is three times that
in the first wire. When a harmonic wave is travelling in the first wire, it is reflected at the junction of the
wires; the reflected wave has half the amplitude of the incident wave. (a) If the amplitude of incident
wave is A, what are the amplitudes of the reflected and transmitted waves? (b) Assuming no loss is
wire, what fraction of the incident power is reflected at the junction and what fraction is transmitted?
(c) Show that the displacement just to the left of the junction equals that just to the right of the junction.
8.
Find the kinetic energy of pulse travelling in a taut string. Given T = 10 N and  = 0.1 kg/m.
UD
Y
7.
ST
[ Give answer in millijoules ]
A 50 cm long wire fixed at both ends vibrates with a fundamental frequency f0 when the tension is 50
N. If the tension is increased to 60 N, the fundamental frequency increases by 5 Hz and a further
increase in tension to 70 N results in a fundamental frequency of (f0 + 9.6) Hz. Determine the mass of
the wire.
10.
A 2 m string is fixed at one end and is vibrating in its third harmonic with amplitude 3 cm and frequency
100 Hz. (a) Write an expression for the kinetic energy of a segment of the string of length dx at a point
x at some time t. At what time is its kinetic energy maximum? What is the shape of the string at this
time? (b) Find the maximum kinetic energy of the string by integrating your expression for part (a) over
the total length of the string.
AC
M
11.
E
9.
How long will it take sound waves to travel the distance  between the points A and B if the air
temperature between them varies linearly from T1 to T2? The velocity of sound propagation in air is
equal to v   T , where  is a constant.
12.
A wave propagates along a medium (along a particular direction) and at a boundary (the separation
between two media) suffers a reflection. Consequently standing wave pattern forms in first medium.
19
The ratio of amplitudes at an antinode and a node is 3. What percentage of energy passes across the
boundary ?
AB is a cylinder of length 1.0 m, fitted with a thin flexible diaphragm C at the middle and two thin
flexible diaphragms A and B at the ends (see figure). The portions AC and BC contain hydrogen and
oxygen respectively. The diaphragms A and B are set into vibrations of the same frequency. What is
the minimum frequency of these vibrations for which the diaphragm C is a node ? Under the conditions
of the experiment, the velocity of sound in hydrogen is 1100 ms 1 and in oxygen is 300 ms 1 .
A
B
C
O2
PO
H2
IN
T
13.
A source of sound revolving in a circle of radius 15 m is emitting a signal of frequency 200 Hz. It
completes one revolution in 3 seconds. Calculate the maximum and minimum frequencies of the signal
heard at a point 30 m from the centre of the circle. (Speed of sound = 330 m/s)
15.
A source of sound with natural frequency v0 moves uniformly along a straight line separated from a
stationary observer by a distance l. The velocity of the source is equal to fraction of velocity of
sound. Find the frequency of sound received by the observer at the moment when the source gets
closest to him and also find the distance between the source and the observer at the moment, when the
observer receives a frequency v = v 0.
16.
A long horizontal pipe is fitted with a piston of mass 10 kg which is connected to another mass
10.5 kg by a string passing over a frictionless pulley. A source of sound of frequency 512 Hz is
placed in front of the piston. Initially the piston is almost in touch with the source and it moves away
from the source when the hanging mass is released. Find the times at which maximum sound will
be heard. Assume the string is horizontal between pulley and piston. There is no friction and velocity
of sound in air is 340 m/s.
17.
A fighter plane is moving in a vertical loop with constant speed of radius R. The center of the loop
is at a height 2R directly overhead of an observer standing on the ground. The observer receives
maximum frequency of the sound produced by the plane when it is nearest to him. Find the speed
E
ST
UD
Y
14.
18.
AC
M
of the plane (in m/s) . Velocity of sound in air is c =
600 3
ms–1.

A man standing in front of a mountain at a certain distance beats a drum at regular intervals. The
drumming rate is gradually increased and he finds that the echo is not heard distinctly when the rate
becomes 40 per minute. He then moves nearer to the mountain by 90 m and finds the echo is again not
heard when the drumming rate becomes 60 per minute. Calculate (a) the distance between the mountain
and the initial position of the man (b) the velocity of sound.
20
EXERCISE-6
NEW IIT-JEE PATTERN QUESTIONS
MULTIPLE CHOICE ANSWER TYPE
At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is
shown Then, which of the following is true regarding the velocities of the points P, Q and R on the
y
string.
Q
(A) vP is upwards
(B) vQ = –vR
x
P
(C) |vP| > |vQ| = |vR|
R
(D) vQ = vR
In a standing wave on a string.
(A) In one time period all the particles simultaneously at rest twice.
(B) All the particle must be at their positive extremes simultaneously once in one time period.
(C) All the particles may be at their positive extremes simultaneously once in a time period.
(D) All the particles are never at rest simultaneously
Figure, shows a stationary wave between two fixed points P and Q. Which points (s) of 1, 2 and 3 are
in phase with the point X ?
3.
(A) 1, 2 and 3
6.
2 3 Q
(C) 2 and 3 only
(D) 3 only
ST
A gas is filled in an organ pipe and it is sounded with an organ pipe in fundamental mode. Choose the
correct statement(s) : (T = constant)
(A) If gas is changed from H2 to O2, the resonant frequency will increase
(B) If gas is changed from O2 to N2, the resonant frequency will increase
(C) If gas is changed from N2 to He, the resonant frequency will decrease
(D) If gas is changed from He to CH4, the resonant frequency will decrease
A clamped string is oscillating in nth harmonic, then :
(A) total energy of oscillations will be n2 times that of fundamental frequency
(B) total energy of oscillations will be (n-1)2 times that of fundamental frequency
(C) average kinetic energy of the string over a complete oscillations is half of that of the total energy
(D) none of these
In the figure, A is an incident pulse and a, b, c, d are the possible forms of the reflected pulse. Tick the
correct answer.
E
5.
1
(B) 1 and 2 only
AC
M
4.
x
UD
P
Y
2.
PO
IN
T
1.
(a)
A
(b)
(A) a is reflected from a rigid wall
(C) c is reflected from a yielding surface
(c)
(d)
(B) b is reflected from a yielding surface
(D) d is reflected from a rigid wall
21
7.
 x
A plane wave y  A sin   t   undergo a normal incidence on a plane boundary separating medium
 v
M1 and M2 and splits into a reflected and transmitted wave having speeds v1 and v2.Then :
A car moves towards a hill with speed vc. It blows a horn of frequency f which is heared by an
observer following the car with speed v0. The speed of sound in air is v.
v
(A) the wavelength of sound reaching the hill is
f
v  vc
(B) the wavelength of sound reaching the hill is
f
 v  v0 
(C) the beat frequency observed by the observer is  v  v  f
c 

PO
8.
IN
T
(A) for all values of v1 and v2 , the phase of transmitted wave is same as that of incident wave.
(B) for all values of v1 and v2 , the phase of reflected wave is same as that of incident wave.
(C) the phase of transmitted wave depends upon v1 and v2.
(D) the phase of reflected wave depends upon v1 and v2 .
Y
2v c (v  v 0 )f
v 2  v c2
A wave equation is given as y = cos(500t –70x), where y is in mm, x in m and t is in sec.
(A) The wave must be a transverse propagating wave.
(B) The speed of the wave is 50/7 m/s
(C) The frequency of oscillations is 1000  Hz.
(D) Two closest points which are in same phase have separation 20/7 cm.
10.
0.8
represents a moving pulse, where x and y are in meter and t in second.Then:
5  (4 x  5t ) 2
(A) pulse is moving in +x direction (B) it will travel a distance of 2.5 m in 2 s.
(C) its maximum displacement is 0.16 m
(D) pulse is moving in –x direction
E
Energy density E of the medium at a distance r from a sound source varies
according to curve shown in figure. Which of the following is/are possible ?
(A) The source may be a point isotropic source.
t
(B) If the source is a plane source, then power of the source is decreasing with time.
(C) If the source is a plane source, then medium particles have damped oscillations.
(D) Density of the medium increases with distance r from the source.
A wave is travelling along a string. At an instant shape of the string is as shown in the enclosed figure.
At this instant, point A is moving upwards. Which of the following statements are correct?
(A) Phase difference between A and C may be equal to 
(B) Displacement amplitude of the wave is equal to the displacement of B at this instant
(C) At this instant velocity of C is also directed upwards
(D) Phase difference between A and C may be equal to /2
12.
AC
M
E
11.
y(x, t) =
ST
9.
UD
(D) the beat frequency observed by the observer is
REASONING TYPE
22
13.
Statement : 1 In case of a standing wave, some energy is transferred past a node
Statement : 2 The energy transferred during incidence is greater than that returning back through
reflected wave and hence net energy transferred past a node is positive.
Statement : 1 The intensity of a plane progressive wave does not change with change in distance from
the source.
IN
T
14.
Statement : 2 The wavefronts associated with a plane progressive wave are planar.
15.
Statement : 1 A balloon filled with CO2 gas acts as a converging lens for a sound wave.
Statement : 2 Sound waves travel faster in air than in CO2.
Statement : 1 Beats are not observed in case of light waves from independent sources.
PO
16.
Statement : 2 The phase difference between two light sources changes randomly.
17.
Statement : 1 A plane progressive harmonic wave is propagating in a string. If tension in the string is
made two times then average power transmitted through the string becomes two times.
2 A 2 F
.
2V
Statement : 1 In a stationary wave, there is on an average no transfer of energy.
UD
18.
Y
Statement : 2 Average power transmission in a string is given by P 
Statement : 2 When two identical waves travelling in opposite directions superimpose, the net
propagation of energy from a place is stopped.
19.
Statement : 1 The speed of sound in solids is maximum though their density is large.
20.
ST
Statement : 2 This is because their coefficient of elasticity is large.
Statement : 1 If two waves of same amplitude, produce a resultant wave of same amplitude, then the
phase difference between them will be 120°.
Statement : 2 Velocity of sound is directly proportional to the square of its absolute temperature.
A closed organ pipe of length 11m is giving a beat of 2Hz when vibrating with tuning fork of frequency
69.5Hz
E
21.
AC
M
Statement : 1 The pipe is giving fourth overtone.
Statement : 2 The pressure wave in pipe is getting a phase of 9  in one round
22.
Statement : 1 Two strings of same length, mass density, and tension are excited to vibrate
with same maximum amplitude, one in a sinusoidal waveform and the other with a triangle
waveform. Both contain the same oscillation energy.
Statement : 2 A 
I
Amplitude of both waves are same, so intensity and hence energy is same for both waves.
LINKED COMPREHENSION TYPE
Write Up-1
23
Superposition of waves results in maximum and minimum of intensities such as in case of standing
waves. This phenomenon is called as interference. Another type of superposition result in interference
in time which is called as beats. In this case waves are analyzed at a fixed point as a function of time.
If the two waves are of nearby same frequency are superimposed, at a particular point, intensity of
combined waves gives a periodic peak and fall. This phenomenon is beats. If w1 and w2 are the
frequencies of two waves then by superimposed y = y1 + y2, we get at x = 0,
IN
T

 w  w 2    w1  w 2 
y  2A cos 1
.t
.t  sin 
2

   2 

Thus amplitude frequency is small and fluctuates slowly. A beat i.e., a maximum of intensity occurs,
also intensity depends on square of amplitude. The beat frequency is given by
PO
Wbeat | w1  w 2 |
Number of beats per second is called as beat frequency. A normal ear can detect only upto 15 Hz of
frequency because of persistence of ear.
If two sound sources of frequency difference 25 Hz are sounded together. Then which of the following
is correct ?
(A) A normal human ear will hear 25 Hz beat frequency
(B) A normal human ear will hear only 10 Hz beat frequency
(C) A normal human ear cannot hear this frequency
(D) A normal human ear can hear maximum of the two frequency sounded together
24.
The phenomena of beats can take place for
(A) Only transverse waves
(C) Both longitudinal & transverse waves
UD
(B) Only longitudinal waves
(D) For sound waves only
The frequency of beats produced air when two sources of sound are activated, one emitting wavelength 32 cm, other 32.2 cm is (Take Vsound = 350 m/s)
(A) 14
(B) 18
(C) 7
(D) 10
ST
25.
Y
23.
A tuning fork of unknown frequency makes 3 beats per second with a standard fork of frequency 384
Hz. The beat frequency decreases when wax is put on prongs of first fork and the frequency of this
fork is
(A) 381 Hz
(B) 387 Hz
(C) 384 Hz
(D) None of the above
Write Up-2
The figure represents the instantaneous picture of a transverse harmonic wave travelling along the
negative x-axis. Choose the correct alternative(s) related to the movement of the nine points shown in
the figure.
27.
28.
29.
30.
AC
M
E
26.
y
B
A
C
H
O
D
E
x
G
F
The points moving upward are :
(A) A
(B) C
(C) F
The points moving downward are :
(A) O
(B) B
(C) D
The stationary points are :
(A) O
(B) B
(C) F
The points moving with maximum velocity are :
(D) G
(D) H
(D) H
24
33.
(D) none of these
For how much time the detector will record the pulse ?
(A) 37.5  10–2 s
(B) 34.5  10–2 s
(C) 31.5  10–2 s
(D) none of these
What is the maximum force applied by the pulse on the wall ?
(A) 400 N
(B) 800 N
(C) 200 N
(D) none of these
Y
32.
When for the first time detector will record the pressure pulse ?
(A) 22  10–2 s
(B) 21  10–2 s
(C) 31.5  10–2 s
UD
31.
PO
IN
T
(A) B
(B) C
(C) D
(D) H
Write Up-3
A plane pressure pulse triangular in shape approaches a rigid wall along normal at a speed of
400 m/s. At time t = 0, situation is shown in the figure. The peak pressure is 100 P. By the wall
pulse gets reflected and pressure near the wall gets doubled. Height of the wall is 2 m and width
is also 2 m. A detector on the wall records a minimum excess pressure of 16 pascal.
Total impulse imparted by the pulse on the wall will be :
(A) 300 Ns
(B) 150 Ns
(C) 750 Ns
(D) none of these
Write Up-4
In the figure, four strings are placed under tension by one or two suspended blocks, all of the
same mass. Strings A, B and C have the same linear density m1 , string D has linear mass density
m2 . The pulleys and strings are frictionless and massless. The velocity of waves in the strings are
vA , vB , vC and vD respectively.
E
ST
34.
36.
m1
, then :
2
(A) vD > vB > vA > vC
(C) vD = vA = vB > vC
(B) vB > vA > vD = vC
(D) vD > (vA = vB) > vC
m1
, then :
2
(A) vD > vC > vB > vA
(C) vB > vA > vC > vD
(B) vA = vB > vD > vC
(D) vA = vB > vC > vD
AC
M
35.
If m2 <
If m1 > m2 >
Write Up-5
One observe that the Doppler effect is not associated with wave motion only but it is a more general
phenomenon and the phenomenon described below is known as “classical Doppler effect”
“ An Indian fighter plane flying at a velocity of 300 m/s on the fighter with a gun which shoots at a rate
25
44.
n
s
i
t
y
1
6
0
g
/
m
Displacement amplitude of wave (in nm) is :
(A) 2.0
(B) 3.0
(C) 5.0
(D) 8.0
If the wave refracts into an another medium with refraction angle twice of the incidence angle which is
very very small, then the equation of wave in second medium in SI units is
ST
43.
e
UD
d
Y
PO
IN
T
of 40 rounds/sec with a muzzle velocity of 1200 m/sec. The shots are aimed at a Pakistani’s plane
flying at a velocity of 200 m/sec. Due to relative motion between the two planes the rate at which bullet
hits the Pakistani plane is different from the rate at which it is shoot from the Indian plane.
37.
Find the rate (in round per sec) at which the bullets hits the Pakistani plane.When the two planes move
in the same direction and the target plane is in front of the Indian plane
(A) 36.67
(B) 43.33
(C) 56.67
(D) 23.33
38.
Find the rate (in round per sec) at which the bullets hits the Pakistanis plane.When the target plane is
behind the shooting plane but moving in the same direction
(A) 36.67
(B) 43.33
(C) 56.67
(D) 23.33
39.
Find the rate (in round per sec) at which the bullets hit the Pakistanis plane.When the two planes move
towards one another
(A) 36.67
(B) 43.33
(C) 56.67
(D) 23.33
40.
Find the rate (in round per sec) at which the bullets hits the Pakistanis plane. When the two planes
move away from one another
(A) 36.67
(B) 43.33
(C) 65.67
(D) 23.33
41.
If the Pakistanis fighter plane starts to move in the perpendicular direction (line joining to planes) when
their separation is 3 km and Indian pilots direct plane always towards the Pakistani plane, the time
after which it will catch the plane is
(A) 18 sec
(B) 16 sec
(C) 3.3 sec
(D) 2.6 sec
Write Up-6
A plane longitudinal wave having frequency 500 rad/s is traveling in positive direction in medium of
3
and of bulk modulus 4 x 104 N/m2. The loudness at a point in the medium is observed
to be 20dB.
42.
The speed of wave is ?
(A) 500 m/s
(B) 250 m/s
(C) 100 m/s
(D) 50 m/s
4
(A) P = 1.2 x 10  Sin 500  t  2 x  
–9
(B) P =  3.0 ×10  Sin 500  t  x  
9
(C) p =  3.0 x 10  Sin 500  t  2 x  
4
(D) P = 1.2 x 10  Sin 500  t  x  
AC
M
E
Write Up-7
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes
S and D are made in the tube at the positions right angle to each other. A source placed at S
generates a wave of intensity I0 which is equally divided into two parts: one part travels along the
longer path, while the other travels along the shorter path. Waves from both the parts meet at the
point D where a detector is placed .
R
S
D
45.
If a maxima is formed at a detector, then. The magnitude of wavelength  of the wave produced
can be given by
(A) R
(B)
R
2
(C)
R
4
(D) All of these
26
46.
If a minima is formed at the detector then, the magnitude of wavelength  of the wave produced can
be given by
(B) 3 R
(C) 52 R
2
The maximum intensity produced at D is given by :
(A) 4 I0
(B) 2 I0
(C) I0
(A) 2R
(D) 3 I0
IN
T
47.
(D) None of these
MATRIX MATCH TYPE
(A)
maximum velocity of a particle at antinode
(B)
maximum velocity of a particle at 5 cm
PO
A string of linear mass density 5 × 10–3 kg/m is stretched under a tension of 72 N between two
rigid supports 60 cm apart. The string is vibrating in second overtone so that amplitude at one of
its antinode is 0.25 cm (values in Column II are in CGS unit)
Column I
Column II
(p)
150
2
(q)
90000 2
2
from any node
(C)
maximum acceleration of a particle
(r)
(150 )
at antinode
(D)
maximum acceleration of particle at
(s)
90000 2
5 cm from any node
A long wire PQR is made by joining two wires PQ and QR of equal radii. PQ has length 4.8m and
mass 0.06Kg. QR has length 2.56m and mass 0.2Kg. The wire PQR is under tension of 80N. A
sinusoidal wave pulse of amplitude 3.5cm is sent along the wire PQ from the end P. No power is
dissipated during the propagation of wave pulse.
ST
49.
UD
Y
48.
Column – II
(p) 1.5
(B) Time taken by pulse to reach from P to R in (102 sec )
(C) Amplitude of reflected wave after incident wave pulse
cross joint Q (in cm)
(D) Amplitude of transmitted wave after the incident
wave pulse cross the joining Q (in cm)
(q) 14
50.
AC
M
E
Column – I
(A) Speed of wave in wire QR (in m/s)
(r) 32
(s) 2.0
A sound wave passes from medium A to a medium B . The velocity of sound in B is greater
than that in A . Assume that there is no absorption or reflection at the boundary. As the wave
crosses the boundary ,
Column -I
Column-II
(A) frequency of sound
(p) will not change
(B) wavelength of sound
(q) can’t be determined
(C) intensity of sound
(r) increase
27
(D) time taken to traverse the same thickness
51.
(s) decrease
Column-I indicates the intensity and amplitude with distance from source of wave in which X
represents either intensity or amplitude. Column-II indicates various wave forms.
Column -I
Column-II
IN
T
X
(A)
(p) spherical
–1
r
X
(q) cylindrical
PO
(B)
r–1
I
(C)
(r) plane
r
Y
I
(D)
(s) none of these
–1
53.
AC
M
(A)
(B)
(C)
(D)
Column (I)
Path 1
Path 2
Path 3
Path 4
ST
Figure shows two sources S1 and S2 that emits radio waves of wavelength  in all directions. The
sources are having phase difference  and are separated by a distance equal to 2.5 . The
vertical line is perpendicular bisector between the sources. If we start at indicated start point and
travel along various paths, what we observe in various paths?
(p)
(q)
(r)
(s)
E
52.
UD
r
Column (II)
maxima all along the path
minima all along the path
alternate maxima and minima on the path
uniform intensity all along the path
In an open end organ pipe; stationary wave is formed as shown in the figure by taking displacement
wave.
1
2 3 4
Column-I
(A) Phase difference is zero between points
Column-II
(p) 2
(B) phase difference is  between points
(q) 3
28
(C) separation between the two point is

2
(r) 1
(D) point at which pressure variation is maximum
A closed organ pipe P1 vibrating in its first overtone and an another open pipe P2 vibrating in its third
overtone are in resonance with the tuning fork of frequency 12Hz
IN
T
54.
(s) 4
In column II, the beats frequency in Hz is given when produced in conditions provided in column I.
Match column I and II.
Column I
(A)
Column II
P1 resonate in 5th harmonic &
(p)
(B)
PO
P2 resonate in 3rd overtone
P1 resonate in 1st overtone and
P2 resonate in 3rd harmonic
(C)
P1 resonate in 9th harmonic and
(q)
3
(r)
8
(s)
12
UD
P1 resonate in 2nd overtone and
P2 resonate in 4th overtone
The pressure equation of a standing wave set up in organ pipe in SI unit is given as
p  2sin  0.1 x  cos 1 t  . In column II, numerical factor is given which is to be choose according
ST
to column I along with SI unit.
Column I
(A)
Separation between node and
antinodes
Temporal phase between points
x  0 and x 
(C)
Displacement of particle at
x  5m
(D)
at
Column II
(p)
0
(q)
3
10
m

E
(B)
AC
M
55.
Y
P2 resonate in 7th overtone
(D)
2
t
(r)
5
1
s
40
Ratio of velocities of particle at
x  10m and x  2.5m at t 
(s)
2
1
s
2
29
PP-10
(D)
2. (C)
5.
(A)
6. (C)
3. (D)
PP-11
1.
5.
(A)
(C)
2. (B)
6. (D)
3. (B)
2. (D)
6. (C)
3. (D)
7. (C)
2. (B)
6. (C)
3. (D)
7. (A)
1.
5.
(D)
(A)
PO
PP-12
(C)
(A)
(B)
Y
PP-13
1.
5.
9.
(C)
(A)
2. (C)
6. (A)
PP-15
(A)
(D)
(B)
2. (B)
6. (B)
10.(C)
ST
1.
5.
9.
PP-16
2. (A)
6. (B)
4. (B)
8. (C)
4. (B)
8. (A)
3. (B)
7. (B)
11. (A)
4. (C)
8. (D)
12. (B)
3. (C)
7. (A)
4. (A)
8. (C)
E
(B)
(B)
4. (C)
8. (C)
AC
M
1.
5.
4. (C)
3. (A)
7. (A)
UD
PP-14
1.
5.
4. (A)
IN
T
1.
30
ANSWER SHEET
Exercise - 02
(A)
2.
(B)
3.
(C)
4.
(A)
5.
(A)
6.
(C)
7.
(B)
8.
(B)
9.
(C)
10. (D)
11. (A)
13.
(D)
14. (A)
15. (C)
17.
(A)
18. (C)
19. (A)
21.
(A)
22. (B)
23. (D)
25.
(C)
26. (A)
27. (A)
28. (C)
29.
(B)
30. (A)
31. (C)
32. (C)
33.
(A)
34. (D)
35. (C)
36. (A)
37.
(C)
38. (C)
39. (D)
40. (B)
41.
(C)
42. (A)
43. (B)
44. (A)
45.
(C)
46. (C)
IN
T
1.
12. (A)
16.
(C)
20. (C)
UD
Y
PO
24. (B)
Exercise - 03
1.
(a) A = 5 mm, (b) l = 7.85 cm, (c) T = 2.095, F = 0.48 Hz displacement y = zero
2.
(a)  = –0.235 m, (b) t0 = 0.745 s
3.
7.26 × 103 kg/m3
5.
30
8.
(b) the even harmonics are missing, (c) 25 Hz, (d) 3rd, 5th, 7th harmonic, (e) 4m
9.

 2   22
 2  12 ,  2  12
12.
684 m/s
17.
20.
(a) v = 1500 m/s, (b) f = 500 Hz, v = 1000 m/s
ST
6.
8m
7.
150
1:2
11.
(a) 75 Hz, (b) 5th, 6th, (c) 2m
13.
f = 163.3 Hz
14.
183 m, 713 Hz
2 uv0
uv
16.
R
3R 
(a)  2 ,  2  , (b)


 6 3 


 6 3   f


525 Hz
18.
442 Hz
E
10.
AC
M
15.
4.
t=0.04s
1
(a) y (cm) 0
-1
-10 -8
-6
-4
-2
0
x(m)
2
4
6
8
10
31
x=0 m
1
y (cm) 0
-1
V = 150 m/s; x = vt;
(b) v p 
x = 150 ×
y
vw
x
vp =
IN
T
-0.10 -0.08 -0.06 -0.04 -0.02 -0.00 0.02 0.04 0.06 0.08 0.10
t(s)
4
 6m
100
1cm
 150m / s
1.5cm
vp = –1 m/s (downwards)
vp
21.
1/48sec 1/24 sec
PO
19.2m/s
t
-19.2m/s
Exercise - 04
2.
3.
6.
7.
8.
Y
3. (C)
7. (D)
11. (D)
UD
(A)
(B)
(C)
(C)
(C)
(B)
(C)
(D)
(A)
(C)
(B)
(D)
(D)
23.
27.
32.
36.
38.
42.
46.
50.
ST
2.
6.
10.
14.
20.
22.
26.
31.
34.
38.
41.
45.
49.
E
1.
(D)
(B)
(B)
(D)
(A)
(C)
(A)
(C)
(C)
(C)
(B)
(A)
(D)
(C)
(A)
(C)
(A)
(D)
(C)
(A)
(C)
4. (C)
8. (D)
12. (A)
24. (A)
28. (A)
39.
43.
47.
51.
(C)
(D)
(A)
(C)
Exercise - 05
(i) 20 m/s, from right to left, (ii) 3 cm, 5.7 Hz, (iii) p/4, (iv) 3.5 m
(a) 20m/s
(b) 2m (c) y  0.02 sin( x  20 t   / 6)
6.258
4.
AC
M
1.
5.
9.
13.
17.
21.
25.
29.
33.
37.
40.
44.
48.
p/2w
5.
25
 x

 x

 100t 
 100 t  , y 2  3 sin 
(a) 10, (b) 3cm, (c) 142.12 J, (d) y1  3 sin 
 10

 10

(a) A r 
0.15 mJ
A
3A
3Pin
, At 
, (b) Pr  Pin / 4, Pt 
, (c) Al = A + Ar = At
2
2
4
9. 9.1 g
2
10.

1 
 3 
–3
dk =  6 sin   x sin 200t  dx; t  2.5  10 s, straight , (b) 89 mJ
2 
 4 

32
t
2
 T1  T2
15.
v
v0
1  2


12. 75
13.
f = 1650 Hz
16. 1.178 sec, 2.04 sec, 2.634 sec etc.
17. 200
Exercise - 06
PO
(C) (D)
4. (B) (D)
(A) (D)
8. (B) (D)
(A) (C)
12. (B) (D)
[A]
[A]
19. [A]
[B]
23. (C)
(B)
27. (A) (D)
(C) (D)
31. (B)
(B)
35. (D)
(A)
39. (C)
(A)
43. (B)
(A)
47. (B)
A - r, B - q, C - p,D - s.
A - p, q, r ,B - p, q, C - p, q, D - s
A -p, q, B -r, s, C -r, s, D -r, s
A - r, B -p, C - p, D -s
Y
3.
7.
11.
15.
18.
22.
26.
30.
34.
38.
42.
46.
49.
51.
53.
55.
E
ST
UD
(C) (D)
2. (A) (C)
(A) (C)
6. (B) (D)
(A) (B) (D)
10. (A) (B) (C)
[D]
14. [A]
[A]
17. [D]
[C]
21. [A]
(C)
25. (B)
(C)
29. (B) (C)
(B)
33. (B)
(B)
37. (B)
(D)
41. (A)
(A)
45. (D)
A-r, B-p, C-s, D-q
A - r, B - q, C - p, D - s
A - q,s, B- p,s C-r ,D -r
A - r, B -q, C-s, D-p
18. 144 Hz and 99 Hz
AC
M
1.
5.
9.
13.
16.
20.
24.
28.
32.
36.
40.
44.
48.
50.
52.
54.
14. 221 Hz, 182.6 Hz
IN
T
11.
33