Physics 198
Exam 3
Fall 2014
41. A string is plucked at 1/3 of its length. Which harmonic is missed?
A)
B)
C)
D)
E)
Second
All even
Third
All odd
Fifth
Solution: Third harmonic should have a node at 1/3 of string’s length, and this is impossible if it
is plucked at this point.
42. Most of the sound from a guitar is emitted by:
A)
B)
C)
D)
E)
Strings
Bridge
Nut
Top and back plates
Fingerboard
Solution: Top and back plates have bigger area than any other part of guitar.
43. What of the following instruments demonstrates chaotic vibrations?
A)
B)
C)
D)
E)
Guitar
Harpsichord
Chimes
Marimba
Cymbals
Solution: Cymbals are known to produce chaotic vibrations.
44. What happens with acoustic impedance of a tube if its cross-sectional area is doubled?
A)
B)
C)
D)
E)
It is doubled
It is halved
It is increased 4 times
It is decreased 4 times
None of the above
Solution:
p
Z
vS
1
Physics 198
Exam 3
Fall 2014
45. What happens to the fundamental frequency of transverse vibrations of a bar if the length of
the bar is doubled?
A)
B)
C)
D)
E)
It is doubled
It is halved
It is increased 4 times
It is decreased 4 times
None of the above
Solution:
For transverse oscillations: f m  vK / 8 L2 m 2 . If length L is doubled, than frequency f is
decreased 4 times.
46. For a free rectangular bar the longitudinal and the transverse fundamentals coincide. What is
the ratio, L/t, of the length, L, to the thickness, t, of this bar?
A)
B)
C)
D)
E)
1.5
2.0
2.5
3.0
4.0
Solution:
For longitudinal oscillations: f n  v  nv / 2 L , where n=1 ,2…
For transverse oscillations: f m  vK / 8 L2 m 2 , where m=3.0112, 5, 7, 9… , and
K  t / 12  t / 3.46
We equate these frequencies, taking smallest values of n=1 and m=3.0112.
vt / 8 12 L2 m 2  v / 2 L  L / t    3 2 / 8 3  2.0


47. Which of the following modes of a piano string has smallest inharmonicity?
A)
B)
C)
D)
E)
Fundamental
First overtone
Second overtone
Inharmonicity of all modes is approximately the same
Answer B or C depending on tension
Solution:
f n  nf1 1  n 2  1A
From this equation follows that inharmonicity is smallest for n=1.


2
Physics 198
Exam 3
Fall 2014
48. If the length of a string is doubled, what happens to the nonlinear shift of the frequency?
A)
B)
C)
D)
E)
It is doubled
It is increased 4 times
It is increased 16 times
It is halved
It is decreased 4 times
Solution:
f n  nf 1 1  n 2  1A

A

 3r 4 E
8TL2
If length of a string, L, is doubled, then the nonlinear shift of the frequency, A, is decreased 4
times.
49. What happens with the distance between the frets on guitar as one moves from the nut to the
bridge?
A)
B)
C)
D)
E)
It decreases
It increases
It remains the same
One of the above depending on the type of guitar
None of the above
Solution:
The interval between successive frets is normally one equal tempered semitone. The ratio of
distances from the fret to the bridge should be 21/12  1.0595 , or approximately 18/17  1.0588 .
In another words; next fret is shifted by approximately 6% of the remaining part. This means that
the distances between the frets decrease.
50. What is popping frequency?
A)
B)
C)
D)
E)
The lowest resonance of a brass instrument mouthpiece
The highest resonance of a brass instrument mouthpiece
The lowest resonance of a wood instrument
The highest resonance of a wood instrument
The frequency shift due to the bell
Solution:
Popping frequency is the lowest resonance of a brass instrument mouthpiece.
3
Physics 198
Exam 3
Fall 2014
51. What happens with the speed and pressure of a fluid flowing through a pipe when it enters a
region in which the cross-sectional area of the pipe increases?
A)
B)
C)
D)
E)
Speed decreases, pressure decreases
Speed decreases, pressure increases
Speed increases, pressure decreases
Speed increases, pressure increases
Speed increases, pressure remains the same
Solution:
When fluid enters a region with bigger area, speed decreases. According to Bernoulli’s equation
smaller speed means bigger pressure.
52. The tension of a circular membrane has been increased by 4 times. What happens to the
frequencies of vibrational modes? The frequencies:
A)
B)
C)
D)
E)
Double
Multiply by a factor of 4
Halve
Multiply by a factor of ¼
Remain the same
Solution:
1 T
f nm 
 nm .
2a 
53. On what instrument will a note sustain as long as the corresponding key is depressed
A)
B)
C)
D)
E)
Upright piano
Grand piano
All types of harpsichords
Some types of harpsichords
Organ
54. Strings of what instrument have the highest tension?
A)
B)
C)
D)
E)
Upright piano
Grand piano
Harpsichords
Violin
Bass
4
Physics 198
Exam 3
Fall 2014
55. What are typical vocal fold vibration frequencies in male and female speakers?
A)
B)
C)
D)
E)
110 and 220 Hz
110 and 440 Hz
220 and 440 Hz
440 and 880 Hz
220 and 880 Hz
56. What is typical frequency of singer’s formant?
A)
B)
C)
D)
E)
500 Hz
1000 Hz
3000 Hz
6000 Hz
10000 Hz
57. Most often, how many formants are enough to disambiguate the vowel?
A)
B)
C)
D)
E)
1
2
3
4
5
58. What is reverberation time?
A)
B)
C)
D)
E)
50 ms after the direct sound when the first group of reflections arrives
80 ms after the direct sound when the first group of reflections arrives
Answer A or B depending on the type of sound (speech or music)
Time it takes for the sound to decay completely
Time it takes for the sound level to decrease by 60 dB
59. If air absorption can be neglected, then the rate at which the sound energy is absorbed
depends on:
A)
B)
C)
D)
E)
The volume of the room
The power of the source
The area and absorption coefficients of all the surfaces in the room
A and B
B and C
Solution: Absorption (effective surface area) A  S1a1  S 2 a2  S 3 a3 ...
5
Physics 198
Exam 3
Fall 2014
60. What happens with reverberation time if absorption is doubled?
A)
B)
C)
D)
E)
Doubled
Multiplied by a factor of 4
Multiplied by a factor of ¼
Halved
Remains the same
Solution:
Reverberation time is given by equation: RT  K
V
A
6