IB Physics I Problem Set—Sound/Standing Waves/Doppler Effect
Read the following Chapters in your Text:
 4.5: “The Doppler Effect”
 4.6: “Standing Waves”
 Glencoe (online text) Chapter 15 “Sound”
Questions/Problems:
(use 343 m/s as the speed of sound for the following questions, unless otherwise noted).
Vocabulary: (Define/describe the following key terms)
1. Compression
2. Rarefaction
3. Doppler effect
4. Standing Wave
5. Resonance
a. Closed-pipe resonance
b. Open-pipe resonance
6. Fundamental (in terms of standing waves)
7. Harmonic
8. Node
9. Antinode
Sound:
1. How can a certain note sung by an opera singer cause a crystal glass to shatter?
2. Why don’t most musical instruments sound like tuning forks?
3. If you shout across a canyon and hear the echo 0.80 s later, how wide is the
canyon?
Doppler Effect:
4. Light from a nearby galaxy is emitted at a wavelength of 657 nm and is observed
on earth at a wavelength of 654 nm. What can we deduce about the motion of this
galaxy? Explain your answer.
5. Explain, with the help of diagrams, the Doppler effect. Show clearly the cases of a
source that (a) moves towards and (b) goes away from a stationary observer as
well as the case of a moving observer.
6. A source approaches a stationary observer at 40 m/s emitting sound of frequency
500 Hz. What frequency does the observer measure?
7. A source is moving away from a stationary observer at 32 m/s emitting sound of
frequency 480 Hz. What frequency does the observer measure?
8. A sound wave of frequency 512 Hz is emitted by a stationary source toward an
observer who is moving away at 12 m/s. What frequency does the observer
measure?
9. A sound wave of frequency 500 Hz is emitted by a stationary source toward a
receding observer. The signal is reflected by the observer and received by the
source, where the frequency is measured and found to be 480 Hz. What is the
speed of the observer?
10. You are in a car traveling at 25.0 m/s toward a pole-mounted warning siren. If the
siren’s frequency is 365 Hz, what frequency do you hear?
Resonance:
11. In what ways does a standing wave differ from a traveling wave?
12. How must the length of an open tube compare to the wavelength of the sound to
produce the strongest resonance?
13. A 440-Hz tuning fork is held above a closed pipe. Find the spacing between the
resonances when the speed of sound in air is 343 m/s.
14. A bugle can be thought of as an open pipe. If a bugle were straightened out, it
would be 2.65-m long.
a. Find the lowest frequency that is resonant for a bugle.
b. Find the next two resonant frequencies for the bugle.
15. The wave velocity of a transverse wave on a string of length 0.500 m is 225 m/s.
a. What is the fundamental frequency of a standing wave on this string if
both ends are kept fixed?
b. While this string is vibrating in the fundamental harmonic, what is the
wavelength of sound produced in air? (take the speed of sound in air to be
330 m/s)
16. A tube with both ends open has two consecutive harmonics of frequency 300 Hz
and 360 Hz.
a. What is the length of the tube?
b. Which harmonics are these? (take the speed of sound in air to be 330 m/s)
IB Questions:
1.
A sound emitting source moves along a straight line with speed v relative to an
observer at rest.
Observer
v
The speed of sound relative to the medium is c. The observer measures the speed of
sound emitted by the source as
A.
c.
B.
c + v.
C.
c – v.
D.
v – c.
(1)
2.
A source of sound moves directly towards a stationary observer. The frequency of
the sound detected by the observer is different from the source frequency because
A.
the loudness of the sound increases as the source moves towards the observer.
B.
the apparent wavelength of the sound is longer.
C.
the speed of sound relative to the observer is increased.
D.
the apparent wavelength of the sound is shorter.
(1)
3.
A pipe, open at both ends, has a length L. The speed of sound in the air in the pipe is
v. The frequency of vibration of the fundamental (first harmonic) standing wave that
can be set up in the pipe is
A.
v
.
2L
B.
L
.
2v
C.
4v
.
L
D.
L
.
4v
(1)
4.
A source of sound emits waves of wavelength λ, period T and speed v when at rest.
The source moves away from a stationary observer at speed V, relative to the
observer. The wavelength of the sound waves, as measured by the observer is
A.
λ + vT.
B.
λ – vT.
C.
λ +VT.
D.
λ – VT.
(1)
5.
Standing waves in an open pipe come about as a result of
A.
reflection and superposition.
B.
reflection and diffraction.
C.
superposition and diffraction.
D.
reflection and refraction.
(1)
6.
A source S produces sound waves of frequency f and is moving along a straight line
as shown below.
I
S
II
IV
III
Which observer I, II, III or IV could hear a sound of frequency f when the source is
in the position shown?
A.
I
B.
II
C.
III
D.
IV
(1)
7.
This question is about the Doppler effect.
The diagram below shows wavefronts produced by a stationary wave source S. The
spacing of the wavefronts is equal to the wavelength of the waves. The wavefronts
travel with speed V.
S
(a)
1
V. In the space below,
2
draw four successive wavefronts to show the pattern of waves produced by
the moving source.
The source S now moves to the right with speed
(3)
(b)
Derive the Doppler formula for the observed frequency f0 of a sound source,
as heard by a stationary observer, when the source approaches the stationary
observer with speed v. The speed of sound is V and the frequency of the sound
emitted by the source is f.
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(3)
The Sun rotates about its centre. The light from one edge of the Sun, as seen by a
stationary observer, shows a Doppler shift of 0.004 nm for light of wavelength
600.000 nm.
(c)
Assuming that the Doppler formula for sound may be used for light, estimate
the linear speed of a point on the surface of the Sun due to its rotation.
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(3)
(Total 9 marks)