1.
A transverse wave travels from left to right. The diagram below shows how, at a particular
instant of time, the displacement of particles in the medium varies with position. Which arrow
represents the direction of the velocity of the particle marked P?
(Total 1 mark)
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2.
The graph shows how the displacement varies with time for an object undergoing simple
harmonic motion.
Which graph shows how the object’s acceleration a varies with time t?
(Total 1 mark)
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3.
Light travels from air into glass as shown below.
What is the refractive index of glass?
A.
sin P
sin S
B.
sin Q
sin R
C.
sin P
sin R
D.
sin Q
sin S
(Total 1 mark)
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4.
Which of the following electromagnetic waves has a frequency greater than that of visible
light?
A.
Ultraviolet
B.
Radio
C.
Microwaves
D.
Infrared
(Total 1 mark)
5.
This question is about simple harmonic oscillations.
A longitudinal wave travels through a medium from left to right.
Graph 1 shows the variation with time t of the displacement x of a particle P in the medium.
Graph 1
(a)
For particle P,
(i)
state how graph 1 shows that its oscillations are not damped.
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(1)
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(ii)
calculate the magnitude of its maximum acceleration.
...........................................................................................................................
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...........................................................................................................................
...........................................................................................................................
(2)
(iii)
calculate its speed at t = 0.12 s.
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...........................................................................................................................
(2)
(iv)
state its direction of motion at t = 0.12 s.
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(1)
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(b)
Graph 2 shows the variation with position d of the displacement x of particles in the
medium at a particular instant of time.
Graph 2
Determine for the longitudinal wave, using graph 1 and graph 2,
(i)
the frequency.
...........................................................................................................................
(2)
(ii)
the speed.
...........................................................................................................................
(2)
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Graph 2 – reproduced to assist with answering (c)(i).
(c)
The diagram shows the equilibrium positions of six particles in the medium.
(i)
On the diagram above, draw crosses to indicate the positions of these six particles
at the instant of time when the displacement is given by graph 2.
(3)
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(ii)
On the diagram above, label with the letter C a particle that is at the centre of a
compression.
(1)
(Total 14 marks)
6.
An object is undergoing simple harmonic motion with light damping. The natural frequency of
oscillation of the object is f0. A periodic force of frequency f is applied to the object. Which of
the following graphs best shows how the amplitude a of oscillation of the object varies with f?
(Total 1 mark)
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7.
The graph shows measurements of the height h of sea level at different times t in the Bay of
Fundy.
Which of the following gives the approximate amplitude and period of the tides?
Amplitude
Period
A.
6.5 m
6 hours
B.
13 m
12 hours
C.
6.5 m
12 hours
D.
13 m
6 hours
(Total 1 mark)
8.
Two waves meet at a point in space. Which of the following properties always add together?
A.
Displacement
B.
Amplitude
C.
Speed
D.
Frequency
(Total 1 mark)
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9.
The graphs show how the acceleration a of four different particles varies with their
displacement x.
Which of the particles is executing simple harmonic motion?
(Total 1 mark)
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10.
The diagram below is a snapshot of wave fronts of circular waves emitted by a point source S at
the surface of water. The source vibrates at a frequency f = 10.0 Hz.
The speed of the wave front is
A.
0.15 cm s–1.
B.
1.5 cm s–1.
C.
15 cm s–1.
D.
30 cm s–1.
(Total 1 mark)
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11.
Two coherent point sources S1 and S2 emit spherical waves.
Which of the following best describes the intensity of the waves at P and Q?
P
Q
A.
maximum
minimum
B.
minimum
maximum
C.
maximum
maximum
D.
minimum
minimum
(Total 1 mark)
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12.
This question is about oscillations and waves.
(a)
A rectangular piece of wood of length l floats in water with its axis vertical as shown in
diagram 1.
The length of wood below the surface is d. The wood is pushed vertically downwards a
distance A such that a length of wood is still above the water surface as shown in diagram
2. The wood is then released and oscillates vertically. At the instant shown in diagram 3,
the wood is moving downwards and the length of wood beneath the surface is d + x.
(i)
On diagram 3, draw an arrow to show the direction of the acceleration of the
wood.
(1)
(ii)
The acceleration a of the wood (in m s–2) is related to x (in m) by the following
equation.
a= −
14
x
l
Explain why this equation shows that the wood is executing simple harmonic
motion.
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...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
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(iii)
The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is
0.70 m.
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...........................................................................................................................
(3)
(b)
The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below,
sketch a graph to show how the velocity v of the wood varies with time over one period
of oscillation.
(1)
(c)
The distance A that the wood is initially pushed down is 0.12 m.
(i)
Calculate the magnitude of the maximum acceleration of the wood.
...........................................................................................................................
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...........................................................................................................................
(2)
(ii)
On your sketch graph in (b) label with the letter P one point where the magnitude
of the acceleration is a maximum.
(1)
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(d)
The oscillations of the wood generate waves in the water of wavelength 0.45 m.
The graph shows how the displacement D, of the water surface at a particular distance
from the wood varies with time t.
Using the graph, calculate the
(i)
speed of the waves.
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...........................................................................................................................
...........................................................................................................................
(2)
(ii)
ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s.
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...........................................................................................................................
(2)
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(iii)
ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s
...........................................................................................................................
...........................................................................................................................
(1)
(Total 15 marks)
13.
Monochromatic light travels from air into water. Which of the following describes the changes
in wavelength and speed?
Wavelength
Speed
A.
increases
decreases
B.
increases
increases
C.
decreases
increases
D.
decreases
decreases
(Total 1 mark)
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14.
Which of the following graphs shows the variation with displacement x of the speed v of a
particle performing simple harmonic motion.
(Total 1 mark)
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15.
A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance
A and released. Its subsequent oscillations have total energy E and time period T.
An identical mass is attached to an identical spring. The maximum displacement is 2A.
Assuming this spring obeys Hooke’s law, which of the following gives the correct time period
and total energy?
New time period
New energy
A.
T
4E
B.
T
2E
C.
2T
4E
D.
2T
2E
(Total 1 mark)
16.
This question is about simple harmonic motion and waves.
(a)
A particle of mass m that is attached to a light spring is executing simple harmonic
motion in a horizontal direction.
State the condition relating to the net force acting on the particle that is necessary for it to
execute simple harmonic motion.
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......................................................................................................................................
......................................................................................................................................
(2)
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(b)
The graph shows how the kinetic energy EK of the particle in (a) varies with the
displacement x of the particle from equilibrium.
(i)
Using the axes above, sketch a graph to show how the potential energy of the
particle varies with the displacement x.
(2)
(ii)
The mass of the particle is 0.30 kg. Use data from the graph to show that the
frequency f of oscillation of the particle is 2.0 Hz.
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(4)
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(c)
The particles of a medium M1 through which a transverse wave is travelling, oscillate
with the same frequency and amplitude as that of the particle in (b).
(i)
Describe, with reference to the propagation of energy through the medium, what is
meant by a transverse wave.
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...........................................................................................................................
...........................................................................................................................
(2)
(ii)
The speed of the wave is 0.80 m s–1. Calculate the wavelength of the wave.
...........................................................................................................................
...........................................................................................................................
(1)
(d)
The diagram shows wavefronts of the waves in (c) incident on a boundary XY between
medium M1 and another medium M2.
The angle between the normal, and the direction of travel of the wavefronts is 30°.
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(i)
The speed of the wave in M1 is 0.80 m s–1. The speed of the waves in M2 is
1.2 m s–1.
Calculate the angle between the direction of travel of the wavefronts in M2 and the
normal.
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...........................................................................................................................
(3)
(ii)
On the diagram, sketch the wavefronts in M2.
(1)
(Total 15 marks)
17.
A cart, connected to two identical springs, is oscillating with simple harmonic motion between
two points X and Y that are equidistant from point O.
The cart is in equilibrium at
A.
all points between X and Y.
B.
point O only.
C.
points X and Y only.
D.
points O, X and Y only.
(Total 1 mark)
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18.
Plane wavefronts are incident on a boundary between two media labelled 1 and 2 in the
diagram.
The diagram of the wavefronts is drawn to scale.
The ratio of the refractive index of medium 2 to that of medium 1 is
A.
0.50.
B.
0.67.
C.
1.5.
D.
2.0.
(Total 1 mark)
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19.
The graph below shows how the displacement x of a particle undergoing simple harmonic
motion varies with time t. The motion is undamped.
Which of the following graphs shows how the total energy E of the particle varies with time t?
(Total 1 mark)
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20.
An orchestra playing on boat X can be heard by tourists on boat Y, which is situated out of
sight of boat X around a headland.
The sound from X can be heard on Y due to
A.
refraction.
B.
reflection.
C.
diffraction.
D.
transmission.
(Total 1 mark)
21.
This question is about simple harmonic motion.
(a)
In terms of the acceleration, state two conditions necessary for a system to perform
simple harmonic motion.
1. ..................................................................................................................................
2. ..................................................................................................................................
(2)
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(b)
A tuning fork is sounded and it is assumed that each tip vibrates with simple harmonic
motion.
The extreme positions of the oscillating tip of one fork are separated by a distance d.
(i)
State, in terms of d, the amplitude of vibration.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
On the axes below, sketch a graph to show how the displacement of one tip of the
tuning fork varies with time.
(1)
(iii)
On your graph, label the time period T and the amplitude a.
(2)
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(c)
The frequency of oscillation of the tips is 440 Hz and the amplitude of oscillation of each
tip is 1.2 mm. Determine the maximum
(i)
linear speed of a tip.
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...........................................................................................................................
...........................................................................................................................
(2)
(ii)
acceleration of a tip.
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(2)
(Total 10 marks)
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22.
Diagram 1 represents equally spaced beads on a spring. The beads are 1 cm apart.
Diagram 1
A longitudinal wave propagates along the spring. Diagram 2 shows the position of the beads at
a particular instant.
Diagram 2
Which of the following is the best estimate of the wavelength?
A.
2 cm
B.
4 cm
C.
8 cm
D.
16 cm
(Total 1 mark)
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23.
The diagram below shows a pulse travelling along a rope from X to Y. The end Y of the rope is
tied to a fixed support.
When the pulse reaches end Y it will
A.
disappear.
B.
cause the end of the rope at Y to oscillate up and down.
C.
be reflected and be inverted.
D.
be reflected and not be inverted.
(Total 1 mark)
24.
Simple harmonic motion and the greenhouse effect
(a)
A body is displaced from equilibrium. State the two conditions necessary for the body to
execute simple harmonic motion.
1.
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.........................................................................................................................
2.
.........................................................................................................................
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(2)
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(b)
In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be
regarded as two masses attached by a spring. A hydrogen atom is much less massive than
the carbon atom such that any displacement of the carbon atom may be ignored.
The graph below shows the variation with time t of the displacement x from its
equilibrium position of a hydrogen atom in a molecule of methane.
The mass of hydrogen atom is 1.7 × 10–27 kg. Use data from the graph above
(i)
to determine its amplitude of oscillation.
.........................................................................................................................
(1)
(ii)
to show that the frequency of its oscillation is 9.1 × 1013 Hz.
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.........................................................................................................................
(2)
(iii)
to show that the maximum kinetic energy of the hydrogen atom is 6.2 × 10–18 J.
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(2)
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(c)
Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of
oscillation f is given by the expression
f=
1
2π
k
,
mp
where k is the force per unit displacement between a hydrogen atom and the carbon atom
and mp is the mass of a proton.
(i)
Show that the value of k is approximately 560 N m–1.
.........................................................................................................................
.........................................................................................................................
(1)
(ii)
Estimate, using your answer to (c)(i), the maximum acceleration of the hydrogen
atom.
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(2)
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(d)
Methane is classified as a greenhouse gas.
(i)
Describe what is meant by a greenhouse gas.
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.........................................................................................................................
.........................................................................................................................
(2)
(ii)
Electromagnetic radiation of frequency 9.1 × 1013 Hz is in the infrared region of
the electromagnetic spectrum. Suggest, based on the information given in (b)(ii),
why methane is classified as a greenhouse gas.
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.........................................................................................................................
(2)
(Total 14 marks)
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