Physics 115 Acoustics
Homework Set #4
Prof. Menningen
1.
Which of the following sound sources produced the depicted
frequency spectrum?
The frequencies are all odd
a. Helmholtz resonator
multiples of 65 Hz, so 65 Hz must
b. closed pipe
be the fundamental frequency and
c. open pipe
the pipe must be closed at one end.
d. string fixed at both ends
2.
Would the combination of four sinusoidal waveforms with
frequencies of 100 Hz, 240 Hz, 733 Hz, and 4000 Hz result in a
complex periodic waveform?
a. Yes, because the frequencies get progressively higher,
resulting in a complex periodic waveform.
p. 1 of 3
b. No, because the sine waves are not all whole-number multiples of a fundamental frequency.
c. It is impossible to say without knowing the relative amplitudes of the frequency components.
d. Yes, as long as the frequencies are positive integers, the resulting waveform will be periodic.
3.
If the following components were combined: 500 Hz, 750 Hz, and 1000 Hz, what would be the
fundamental frequency?
a. 25 Hz
Choose the largest common factor,
b. 500 Hz
which is 250 Hz in this case.
c. 250 Hz
d. 50 Hz
4.
The sound you hear from a moving horn has a higher frequency than the sound produced by the
horn. Which of the following is true?
a. A second horn is producing a beat frequency that is higher than the original horn.
b. The horn is moving toward you.
c. The horn is moving away from you.
d. The sound waves from the horn are diffracting with a higher frequency.
5.
If you move away from a stationary source of sound, the frequency you hear is ______ the
frequency produced by the source.
a. higher than
b. lower than
c. equal to
6.
You are heading away from an island in your speedboat, while your friend waves goodbye from the
shore. You sound the boat’s horn to say goodbye. The wavelength of the sound produced by the
horn is _____ the wavelength of the sound heard by your friend.
a. longer than
b. shorter than
c. equal to
7.
The image at right shows a complex waveform that is produced
by 1.00sin(ωt) plus a second sine wave. Use the Fourier
Synthesis applet (RIGHT click on the following link and choose
"Open in new window": http://www.falstad.com/fourier/ ) to
find the frequency of the second sine wave.
a. ω t
b. 2ω t
c. 3ω t
d. 4ω t
e. 5ω t
f. 6ω t
Physics 115 Acoustics
Homework Set #4
Prof. Menningen
p. 2 of 3
Numerical questions
1.
The image at right shows a complex waveform that is produced
by 1.00sin(ωt) plus a second sine wave. Use the Fourier
Synthesis applet (RIGHT click on the following link and choose
"Open in new window": http://www.falstad.com/fourier/) to find
the amplitude of the second sine wave. You will have to note the
shape of the waveforms very carefully. Note that the horizontal
lines in the applet are at −1.00 and +1.00, but the lines in the
image above are spaced every 0.50. There is a larger than usual
tolerance to the accepted answers, but you will need to get reasonably
close.
The waveform was generated from 1.00sin(ω t) – 0.60sin(3ω t), but the homework system
was programmed to accept any amplitude between −0.53 and −0.87 for the sin(3ω t)
wave. That range of values produced waveforms reasonably similar to the one shown.
2. A resonating pipe produced the frequency spectrum shown in the figure at
right. If the speed of sound is 343.8 m/s, what is the length of the pipe?
The tube is closed at one end, so the wavelength
of the fundamental standing wave is 1  4 L. Thus
f 
c


c
4L
L
c 343.8 m/s

 1.3 m
4 f 4  65 Hz 
That's equivalent to about 4 feet, 4 inches
3. If a 750-Hz sound source travels toward a listener with a velocity of 50 mph (miles per hour), what
is the frequency of the sound heard by the listener? In this case the speed of sound is 348 m/s.
The source is moving toward a listener at rest:
mi 1609 m
1h


 22.3 m/s
h
1 mi
3600 s


cair
 348 m/s

 fsource 
   750 Hz  
  801 Hz
c

v
348

22.3
m/s


 air source 
vsource  50
f listener
Physics 115 Acoustics
Homework Set #4
Prof. Menningen
p. 3 of 3
4. If a sound source is moving with a velocity of 31 m/s away from a listener and the sound source is
producing a 775-Hz tone, what is the sound frequency perceived by the listener? The speed of sound
in this case is 342 m/s.
The source is moving away from a listener at rest:


cair
 342 m/s 
f listener  fsource 
   775 Hz  
  711 Hz
c

v
342

31
m/s


source 
 air
5. If a listener is moving with a velocity of 14 m/s toward a sound source producing a 1600-Hz tone
and simultaneously the sound source is moving toward the listener with a velocity of 22 m/s, what is
the perceived frequency of the sound? The speed of sound in this case is 340 m/s.
Both the source and the listener are moving toward one another, so
choose the upper sign in each case:
 c  vlistener
f listener  fsource  air
 cair  vsource

 340  14 m/s 
  1600 Hz  
  1781 Hz
 340  22 m/s 

6. A trumpet player, at rest, is playing a note with a frequency of 440.00 Hz. How fast would you have to
move toward this player to measure a frequency of 463.92 Hz? Report your answer in miles per hour
(1 mile = 1609 meters, use "mph" as your unit symbol). In this case the speed of sound is 338 m/s.
The source is at rest and the listener is moving toward it. Solve for v:
 c  vlistener 
f listener  fsource  air

cair


cair
f listener  cair  vlistener
fsource
f

 463.92 Hz 
cair  listener  1  vlistener   338 m/s  
 1  18.37 m/s
 440.00 Hz 
 fsource

m
1 mi
3600 s
18.37


 41.1 mph
s
1609 m
1h