- 3-1
- A travelling wave on a string is described by

where and are in centimetres and is in seconds (a) for , plot as a function of for . (b) Repeat (a) for and . (c) From your graphs, what is the wave speed, and in which direction ( or ) is the wave travelling? - 3-2
- What is the fastest transverse wave that can be sent along a steel
wire? Allowing for a reasonable safety factor, the maximum tensile
stress to which stress to which steel wires should be subject is
.
The density of steel is
.
Show that your answer does not depend on
the diameter of the wire.
- 3-3
- A series of pulses, each of amplitude 0.150 m, are sent
down a string that is attached to a post at one end. The pulses are
reflected at the post and travel back along the string without loss of
amplitude. What is the displacement at a point on the string where
two pulses are crossing (a) if the string is rigidly attached to the
post? (b) If the end at which reflection occurs is free to slide up
and down?
- 3-4
- A transverse sinusoidal wave on a string has a period
and travels in the negative direction with a speed of . At
, a particle on a string at has a displacement of and
travels downward with a speed of . (a) What is the amplitude of
the wave? (b) What is the initial phase angle? (c) What is the
maximum transverse speed of the string? (d) Write the wave function
for the wave.
- 3-5
- An acoustic microscope can form a remarkably detailed
image of microelectronic circuits such as transistors. The sound waves
have a frequency of . The speed of such waves in the
liquid helium in which the specimen is immersed is . (a)
What is the wavelength of these ultra-high-frequency acoustic waves?
(b) You wish to take images of circuits of conductors that are
approximately wide. To how many wavelengths does this
correspond?
- 3-6
- A sinusoidal sound wave is described by the displacement

(a) find the amplitude, wavelength and speed of this wave. (b) Determine the instantaneous displacement of the molecules at the position at . (c) Determine the maximum speed of the molecule's oscillator motion. - 3-7
- Two identical travelling waves, moving in the same direction, are out
of phase by . What is the amplitude of the combined wave in terms
of the common amplitude of the two combining waves?
- 3-8
- Two loudspeakers, and , are 7.0 m apart. Each
emits a sound frequency of 200 Hz, uniformly in all directions.
has an acoustic output of
and one of
. and
vibrate in phase. Consider a point that is 4.0 m from and 3.0
m from . (a) How are the phases of the two waves arriving at
related? (b) What is the intensity of sound at with both and
on? (c) What is the intensity of sound at if is turned
off ( on)? (d) What is the intensity of sound at if is turned
off ( on)?
- 3-9
- A 15-cm violin string, fixed at both ends, is vibrating in
its mode. The speed of waves in this wire is 250 m/s,
and the speed of sound in air is 348 m/s. What
are (a) the frequency and (b) the wavelength of the emitted sound wave?
- 3-10
- A 75 cm string is stretched between fixed supports. It is
observed to have resonant frequencies of 420 and 315 Hz, and no other
resonant frequencies between the two. (a) What is the lowest resonant
frequency for this string? (b) What is the wave speed for this string?
- 3-11
- A tuning fork of unknown frequency makes 3 beats per
second with a standard fork of frequency 384 Hz. The beat frequency
decreases when a small piece of wax is put on a prong of the first
fork. What is the frequency of this fork?
- 3-12
- A string 2.7 m long has a mass of 260 g. The tension in
the string is 36 N. What must be the frequency of travelling waves of
amplitude 7.7 mm in order that the average transmitted power be 85 W?
- 3-13
- A vacuum cleaner has a measured sound level of 70 dB. (a)
What is the intensity of this sound in watts per square meter? (b)
What is the pressure amplitude of this sound?
- 3-14
- A whistle used to call a dog has a frequency of 30 kHz.
The dog, however, ignores it. The owner of the dog, who cannot hear
sounds above 20 kHz, wants to use the Doppler effect to make certain
that the whistle is working. She asks a friend to blow the whistle
from a moving car, while the owner remains stationary and listens. (a)
How fast must the car move and in what direction? Is the experiment
practical? (b) Repeat for a whistle frequency of 22 kHz instead of 30
kHz.
- 3-15
- The ``red shift'' of radiation from a distant galaxy
consists of the light , known to have a wavelength of 434 nm when
observed in the laboratory, appearing to have a wavelength of 462
nm. (a) What is the speed of the galaxy in the line of sight relative
to the earth? (b) Is it approaching or receding?