Physics 115 Acoustics
Homework Set #3
Prof. Menningen
p. 1 of 3
1.
A wave interference pattern is produced by two sources of sound that are in phase with each other.
As the frequency of the sound increases, the separation of the antinodal lines in the interference
pattern will ________.
a. decrease
b. increase
c. remain the same
2.
Why don't we hear beats when adjacent keys on a piano are hit at the same time?
a. Beats can only be produced by longitudinal waves, not the transverse waves that occur in
piano strings.
b. The different speeds of the sound waves from each piano key scrambles the beat pattern so
that we cannot hear it.
c. The beats do exist, but the beat frequency is too high for us to notice.
d. Destructive interference between the sound waves from each piano key removes the beat
pattern.
3.
Two strings carry waves of the same frequency. String A has more mass per unit length than string
B. The wavelength of the waves on string A will be ______ than the wavelength of the waves on
string B because the wave speed on string A is ______ than the wave speed on string B.
a. longer ... slower
b. shorter ... faster
c. longer ... faster
d. shorter ... slower
4.
The wavelength of the third harmonic standing wave on a string that is fixed at both ends is _____
the length of the string.
a. three-fourths
b. three times
c. one and a half times
d. two-thirds
5.
When a sound wave travels from a narrow tube into a wide tube, the specific acoustic impedance it
encounters ______ and the acoustic impedance ______.
a. decreases … stays the same
b. increases … decreases
c. stays the same … increases
d. stays the same … decreases
6.
You have an organ pipe that resonates at frequencies of 300, 450, and 600 hertz but nothing inbetween. It may resonate at lower and higher frequencies as well. Is the pipe open at both ends or
open at one end and closed at the other?
The fundamental frequency
a. These frequencies are impossible for any kind of organ pipe. is 150 Hz and the three
b. It could be either kind of organ pipe.
frequencies are the 2nd, 3rd,
c. open at both ends
d. open at one end and closed at the other
and 4th harmonics.
7.
What happens to the fundamental frequency of an organ pipe as the temperature in the room
decreases?
a. The fundamental frequency increases.
b. The wave speed will decrease, but the wavelength will increase and the fundamental
frequency will not change.
c. The speed, wavelength, and frequency are independent of
temperature.
d. The fundamental frequency decreases.
8.
The typical human ear has a canal length of 2.4 cm. If a person's ear
canal is shorter than 2.4 cm, the fundamental frequency of that person's
ear canal will be _____ that of the typical ear.
a. higher than
b. lower than
c. the same as
Physics 115 Acoustics
Homework Set #3
Prof. Menningen
p. 2 of 3
Numerical questions
1. A 4.5-m length of rope, with a mass of 0.52 kg, is pulled taut with a tension of 45 N. Find the speed
of waves on the rope.
v
F


F
FL


mL
m
 45 N  4.5 m   19.7 m/s
 0.52 kg 
2. A 5.2-m wire with a mass of 91 grams is attached to the mast of a sailboat. If the wire is given a
"thunk" at one end, it takes 0.085 s for the resulting wave to reach the other end. What is the tension
in the wire?
distance L 5.2 m
 
 61.18 m/s
time
t 0.085 s
F
FL
FL
mv 2
2
v

v 

F

m
m
L
v
mv 2  0.091 kg  61.18 m/s 
F

 65.5 N
L
5.2 m
2
3. A string 1.1 m long with a mass of 2.6 grams is stretched between two fixed points with a tension of
99 N. Find the frequency of the fundamental standing wave on this string.
1  2 L  2 1.1 m   2.2 m
v
F

c f

FL

m
 f 
c

 99 N 1.1 m   204.7 m/s
 0.0026 kg 

204.7 m/s
 93.0 Hz
2.2 m
4. The speed of waves on a string that is tied down at both ends is 31 m/s. If the fundamental frequency
for this string is 58 Hz, what is the length of the string?
1 
c 31 m/s

 0.534 m
f 58 Hz
1  2 L  L 
1
2

0.534 m
 0.267 m
2
Physics 115 Acoustics
Homework Set #3
Prof. Menningen
p. 3 of 3
5. Two strings that are fixed at each end are identical, except that one is 0.525 cm longer than the other.
Waves on these strings propagate with a speed of 32.4 m/s, and the fundamental frequency of the
shorter string is 222 Hz. What beat frequency is produced if each string is vibrating with its
fundamental frequency?
f1, A 
c
2 LA
 LA 
c
32.4 m/s

 0.0730 m
2 f1, A 2  222 Hz 
LB  LA  0.00525 m  0.0782 m
f1, B 
c
32.4 m/s

 207.2 Hz
2 LB 2  0.0782 m 
f beat  f1,A  f1,B  222 Hz  207.2 Hz  14.8 Hz
6. The organ pipe pictured above is 3.05 m long. What is
the frequency of the standing wave shown in the pipe?
(Assume the speed of sound is 343 m/s.)
4
3
c
4
 3.05 m   4.067 m
3
343 m/s
f3 

 84.3 Hz
 3 4.067 m
3  L 
7. The frequency of the standing wave shown in the
figure above is 886 Hz. What is the fundamental
frequency of this pipe? 443 Hz
The pictured wave is the second harmonic. It has
twice the frequency of the fundamental.
f 2  2 f1  f1 
f 2 886 Hz

 443 Hz
2
2
8. The human ear canal is much like an organ pipe that is closed
at one end (at the tympanic membrane or eardrum) and open
at the other (see the figure above). A person's ear canal has a
length of d = 2.14 cm. What is the fundamental frequency of
this person's ear canal? (Assume the speed of sound is 343
m/s.) 4007 Hz
1  4 L  4  0.0214 m   0.0856 m
f1 
c
1

343 m/s
 4007 Hz
0.0856 m