Oscillators
1. Hecht3 10.MC.022. [184746]
Two coiled springs are made of the same wire such that they are identical in all respects,
except the first is half the length of the second. Compared to the natural frequency of the first
(f), the natural frequency of the second is
2f
f
none of these
f/
1/2f
2. Hecht3 10.MC.023. [184747]
The free end of a clamped saw blade vibrates 12.8 times in 19 s. Its frequency is
12.8 Hz
1.48 Hz
none of these
0.67 Hz
19 Hz
3. Hecht3 10.MC.025. [184749]
An adult and a child are sitting on adjacent identical swings. Once they get moving, the adult,
by comparison to the child, will necessarily swing with
a much greater frequency
the same period
the same amplitude
a much greater period
none of these
actually slightly lower because of higher
CM
4. Hecht3 10.MC.028. [184752]
Sometimes a really heavy truck will go by and set the windows of the house vibrating for a
moment with a low-frequency buzz. They oscillate
in-phase with the truck due to critical damping
none of these
in an undamped mode
at one of their natural frequencies
at a random changing frequency
5. Hecht3 10.MC.033. [184755]
Astronauts in space took a light, coiled spring of known elastic spring constant, attached a
mass to it, and set it oscillating. Measuring the period, they could determine
the time of day
the weight of the bob
the acceleration due to gravity
none of these
the mass of the bob
6. Hecht3 10.P.066. [184777]
The respiratory system of a medium-sized dog resonates at roughly 5 Hz so that it can pant
(in order to cool off) very efficiently at that frequency. How many breaths will the dog be taking
in 1.4 minutes? For comparison, the dog would ordinarily breathe at around 30 breaths per
minute.
6a
420
breaths
7. Hecht3 10.P.068. [184779]
A hovering fair-sized insect rises a little during the downstroke of its wings and
essentially free-falls slightly during the upstroke. The end result is that the creature
oscillates in midair. If it typically falls about 0.20 mm per cycle, what is the wing beat
period and frequency? (Compare that to the 10 Hz oscillation of a butterfly, which
cannot hover.)
7a
7b
.125
8
s (beat period) T = 2(√[2gh]) = 2√[2(9.8)(2E-4)] =
Hz (frequency)
8. Hecht3 10.P.073. [184781]
A body oscillates in SHM according to the
equation x = 4.8 cos (0.40t + 0.10) where each
term is in SI units.
(a) What is the amplitude at t = 0?
4.8
8a
m
(b) What is the frequency at t = 0?
0.064
8b
Hz
(c) What is the initial phase at t = 0?
0.1
8c
rad
(d) What is the displacement at t = 2.1 s?
8d
2.83
m
9. Hecht3 10.P.087. [184785]
A bug having a mass of 0.18 g falls into a spider's web, setting it into vibration with a dominant
frequency of 21 Hz. Find the corresponding elastic spring constant.
9a
3.13
N/m 2πf = √[k/m]
10. Hecht3 10.P.086. [184784]
A 0.8 N bird descends onto a branch that bends and goes into SHM with a period of 0.51 s.
Determine the effective elastic force constant for the branch.
10a
12.4
N/m
2π/T = √[k/m]
11. Hecht3 10.P.111. [184792]
How long must a simple pendulum be if it is to have a period of 7.5 s? [Hint: The period of a
simple pendulum is proportional to the square root of the length.]
11a
14
m
2π/T = √[g/l]
12. Hecht3 10.P.112. [184793]
While standing on a distant planet it is found that a 2.00 m long pendulum has a period of
11.00 s. What is the acceleration due to gravity on that planet?
12a
0.64
m/s2 T = 2π√[l/g]
WAVES 1
1. Hecht3 11.DQ.001. [184796]
Imagine two symmetrical pulses that are identical in every way, except that one is inverted.
These pulses are moving toward each other on a rope in opposite directions. What happens to
the energy of the rope at the instant of complete cancellation?
The waves vanish, which certainly means there is no elastic PE stored in the undistorted rope.
All the energy is kinetic, though undisplaced at that very instant the various segments of the
rope in the region of overlap are nonetheless moving vertically.
2. Hecht3 11.DQ.004. [184799]
Picture a long row of standing dominos, one a little behind the other so that knocking over the
first will knock over the second and so on. Now imagine an idealized tube an inch or two in
diameter extending from New York to California. Suppose this tube is filled with greased,
essentially frictionless marbles and you push one more in at the East Coast end only to have
one pop out at the West Coast end. What's happening, and how do these arrangements of
dominos and marbles relate to this chapter?
These are both systems that propagate energy and momentum via a disturbance of a medium.
The dominos utilize gravity, a little like long-wavelength liquid surface waves, while the marbles
from an elastic medium. In neither case is the medium substantially displaced. Thus in the
broadest sense both of these disturbances constitute waves.
3. Hecht3 11.DQ.009. [184803]
As an orchestra literally warms up, its sound changes. What do you think happens to the pitch
of the strings and the wind instruments as a result of their being played for a while? Explain.
The strings warm from the friction so they expand. There is a decrease in tension and a drop in
speed and frequency. The wind instruments warm from breath, increasing v and therefore f.
4. Hecht3 11.DQ.013. [184807]
As a rule, instruments such as the piano that utilize struck strings will arrange to have the
striking take place at a point 1/7th of the way down the string. Considering the fact that the 7th
harmonic is generally unpleasantly dissonant, explain why the strings are struck where they
are.
The answer lies in Young's Law of Strings (1800), which was discussed though not under its
formal name. Remember that the point at which the string is struck must be an antinode
because it is vibrating with maximum amplitude there. But the 7th harmonic has 7 antinodes
and divides the string into 7 equal-length segments. Thus, 1/7th of the way down the string
oscillating in the 7th harmonic, there must be a node. Hence, if we strike a string at that 1/7th
distance, we preclude the presence of the unpleasant 7th harmonic.
5. Hecht3 11.DQ.015. [184809]
The tuning fork, which was invented in 1712 by John Shore, Handel's trumpeter, can vibrate
(Fig. Q15) briefly in a mode that produces its first overtone, or clang tone, at a frequency of
6.27 times the fundamental. If you wish to have the fork produce a nearly pure tone and so
suppress the high-pitched clang tone, where should it be struck? Explain.
Tuning forks should be struck at the location of the node in the clang mode, roughly a third of
the way down from the end. That would put an antinode there making the first overtone
impossible. The fork is essentially a bent rod with the same first overtone.
6. Hecht3 11.MC.007. [184815]
The speed of a wave on a stretched string _____ when the tension in it is doubled.
doubles
decreases by a factor of 2
increases by a factor of 1.414
none of these
increases by a factor of 4
7. Hecht3 11.MC.008. [184816]
Two strings of the same length are being used in a wave experiment. The first, which has twice
the mass of the second, is stretched twice as taut as the second. The speed of the first's wave
is
twice that of the second
the same as the second
less than the second by
greater than the second by
none of these
8. Hecht3 11.MC.009. [184817]
A periodic wave passes an observer, who records that there is a time of 0.5 s between crests.
the frequency is 0.5 Hz
the period is 0.5 s
the wavelength is 0.5 m
none of these
the speed is 0.5 m/s
9. Hecht3 11.MC.011. [184819]
For a harmonic wave of a certain type in a given medium, doubling the frequency has the effect
of
halving the speed
doubling the period
halving the wavelength
none of these
doubling the amplitude
10. Hecht3 11.MC.015. [184821]
Quite generally, doubling the amplitude of a wave
doubles the frequency
doubles the speed
quadruples the energy
none of these
halves the period
11. Hecht3 11.MC.016. [184822]
The speed of sound in air at 40°C by comparison to the speed at 0°C is
much lower
the same
none of these
higher
a little lower
12. Hecht3 11.MC.019. [184825]
A sound that has an intensity-level of 100 dB is how many times more intense than a sound of
20 dB?
5
1000
12a
none of these
108
8
13. Hecht3 11.MC.021. [184827]
A sound-level meter placed in front of the loudspeaker of a 60 W audio system reads 70 dB.
All else being equal, when placed in front of a 120 W system, the meter will read
120 dB
63 dB
13a
none of these
73 dB
140 dB
14. Hecht3 11.MC.022. [184828]
In order to cause the loudness of a sound to appear half its original value, it must be
increased by 50 dB
decreased by 3 dB
none of these
decreased by 10 dB
decreased by 50 dB
15. Hecht3 11.MC.023. [184829]
A doubly-open organ pipe, in comparison to a singly-open pipe of the same length, has a
fundamental frequency that is
half as great
1/π times smaller
none of these
twice as great
three times larger
16. Hecht3 11.MC.024. [184830]
The flute and piccolo are in the same family of instruments, and each functions as a pipe
open at both ends. Both have the same fingering but different lengths. The flute is about 66
cm long and is an octave lower than the piccolo-that is, the piccolo plays at twice the
frequency of the flute. It follows that the piccolo, in comparison to the flute, is about
twice as long
as long
the same length
none of these
half as long
eight times
17. Hecht3 11.MC.030. [184836]
Two tuning forks of frequency 380 Hz and 384 Hz are excited simultaneously. The resulting
sound will waver in intensity with a frequency of
382 Hz
2 Hz
none of these
4 Hz
0
18. Hecht3 11.P.001. [184838]
Figure P1 shows two views -- (a) optical and (b) acoustical -- of a computer circuit. The
acoustic microscope has the highly desirable ability to see several micrometers below the
surface. The device focuses ultrasonic waves at a frequency of 3 GHz through a droplet of
water onto the object. The speed of the waves in the water, which couples the microscope to
the specimen, is 1.5 km/s. Compute the wavelength of the radiation.
18a
500
nm v = fλ, λ = v/f = (1.5E3 m/s)/(3E9 /s) = 0.5 x 10-6 m = 500 nm
19. Hecht3 11.P.003. [184840]
An A note of 440 Hz is played on a violin submerged in a swimming pool at the wedding of
two scuba divers. Given that the speed of compression waves in pure water is 1498 m/s,
what is the wavelength of that tone?
19a
3.40
m λ = v/f = (1498 m/s) /(440 /s)=3.40m
20. Hecht3 11.P.004. [184841]
A wave on a string travels an 8 m length in 2.1s. A harmonic disturbance of wavelength
0.50 m is then generated on the string. What is its frequency?
20a
7.6
Hz f = v/ λ = (8m/2.1s)/0.5m = 7.6 Hz
21. Hecht3 11.P.008. [184842]
The speed of a sinusoidal wave is 3.90 m/s, and its profile is specified by the expression y
= (11 cm) sin [2πx/(0.0314 cm)]. Determine its period.
21a
.805
µs
f = v/ λ = 1/T or T = λ /v = (3.14E-4 m)/(390 m/s)= 0.805 μs
22. Hecht3 11.P.044. [184851]
According to folklore one can best listen for trains, out in the countryside, by putting an ear
to the rails. Steel track has a density of 7.8 103 kg/m3 and a Young's Modulus of 200 GPa.
What is the speed of compression waves in the track (the speed of sound in air is 330
m/s)?
22a
km/s v = √[Y/ρ] = √[2E11/7.8E3] = 5064 m/s
23. Hecht3 11.P.047. [184853]
An underwater explosion occurs in a fresh water lake. What is the speed of the resulting
compression wave if the Bulk Modulus of water is 2.0 GPa? [Hint: When treating liquids the
wave speed is determined by the Bulk Modulus and the density.]
23a
km/s v = √[B/ρ] = √[2E9 Pa/1E3 kg/m3] = 1.4 km/s