Question 1

The path difference between two waves is 5m. If the wavelength of the waves emitted by the two sources is 4m, what is the phase difference (in degrees)?

Accepted Answer

A)  90 
B)  400 
C)  1.57 
D)  7.85 
E)  15 
A)  90 
B)  400 
C)  1.57 
D)  7.85 
E)  15 A

Question 2

If a supersonic plane is flying at increasing speed as the temperature decreases, what happens to the Mach number in this instance?

Accepted Answer

A)  It stays the same. 
B)  It increases. 
C)  It decreases. 
D)  It can do any of the above. 
E)  It can do either (a) or (b) but not (c). 
A)  It stays the same. 
B)  It increases. 
C)  It decreases. 
D)  It can do any of the above. 
E)  It can do either (a) or (b) but not (c). B

Question 3

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

Accepted Answer

A)  x = 0, 1.0 m, 2.0 m 
B)  x = 0.50 m, 1.5 m 
C)  x = 0.50 m, 1.0 m, 1.5 m 
D)  x = 0.75 m, 1.25 m 
E)  x = 0.25 m, 0.75 m, 1.25 m, 1.75 m 
A)  x = 0, 1.0 m, 2.0 m 
B)  x = 0.50 m, 1.5 m 
C)  x = 0.50 m, 1.0 m, 1.5 m 
D)  x = 0.75 m, 1.25 m 
E)  x = 0.25 m, 0.75 m, 1.25 m, 1.75 m D

Question 4

Two waves are described by y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters).
With what angular frequency does the maximum amplitude of the resultant wave vary with time?

Accepted Answer

A)  366 rad/s 
B)  6 rad/s 
C)  3 rad/s 
D)  92 rad/s 
E)  180 rad/s 
A)  366 rad/s 
B)  6 rad/s 
C)  3 rad/s 
D)  92 rad/s 
E)  180 rad/s

Question 5

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

Accepted Answer

Question 6

As shown below, a garden room has three walls, a floor and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is

Accepted Answer

A) 
  , where n is a positive integer. 
B) 
  , where n is an odd integer. 
C) 
  , where n is an even integer. 
D)  in all cases listed above. 
E)  given by (a) or (b) above, but not by (c). 
A) 
  , where n is a positive integer. 
B) 
  , where n is an odd integer. 
C) 
  , where n is an even integer. 
D)  in all cases listed above. 
E)  given by (a) or (b) above, but not by (c).

Question 7

Two harmonic waves are described by     From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

Accepted Answer

A)  3 
B)  0.25 
C)  0 
D)  6 
E)  1.5 
A)  3 
B)  0.25 
C)  0 
D)  6 
E)  1.5

Question 8

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

Accepted Answer

A)  440, 880 and 1 320 Hz. 
B)  660, 1 320 and 1 980 Hz. 
C)  880, 1 320 and 1 760 Hz. 
D)  1 320, 2 640 and 3 960 Hz. 
E)  They have no overtones in common. 
A)  440, 880 and 1 320 Hz. 
B)  660, 1 320 and 1 980 Hz. 
C)  880, 1 320 and 1 760 Hz. 
D)  1 320, 2 640 and 3 960 Hz. 
E)  They have no overtones in common.

Question 9

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?

Accepted Answer

A)  3.14 m 
B)  1.00 m 
C)  6.28 m 
D)  12.0 m 
E)  2.00 m 
A)  3.14 m 
B)  1.00 m 
C)  6.28 m 
D)  12.0 m 
E)  2.00 m

Question 10

Two ropes are spliced together as shown.   A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 11

A source of sound waves is placed at the center of a very large sound-reflecting wall. The source emits 0.500 W of power. Two meters from the source the intensity in W/m2 is

Accepted Answer

A)  9.95 × 10−3. 
B)  1.99 × 10−2. 
C)  0.313. 
D)  0.399. 
E)  0.625. 
A)  9.95 × 10−3. 
B)  1.99 × 10−2. 
C)  0.313. 
D)  0.399. 
E)  0.625.

Question 12

The superposition of two waves,   and   , results in a wave with a phase angle of

Accepted Answer

A)  0 rad. 
B)  0.5 rad. 
C) 
  rad. 
D) 
  rad. 
E)  π rad. 
A)  0 rad. 
B)  0.5 rad. 
C) 
  rad. 
D) 
  rad. 
E)  π rad.

Question 13

Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

Accepted Answer

A)  0.800, 0.670, 0.500 
B)  1.33, 1.00, 0.500 
C)  2.00, 1.00, 0.500 
D)  2.00, 1.33, 1.00 
E)  4.00, 2.00, 1.00 
A)  0.800, 0.670, 0.500 
B)  1.33, 1.00, 0.500 
C)  2.00, 1.00, 0.500 
D)  2.00, 1.33, 1.00 
E)  4.00, 2.00, 1.00

Question 14

The intensity level of an orchestra is 85 dB. A single violin achieves a level of 70 dB. How does the intensity of the sound of the full orchestra compare with that of the violin?

Accepted Answer

The answer of The intensity level of an orchestra is...

Question 15

A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0° C. The speed of sound in sea water is 1 533 m/s. How much earlier (in s) does a dolphin 1 000 m from the source hear the sound than a person in a boat that is also 1 000 m distant? (Ignore the time it takes the sound to reach the water surface.)

Accepted Answer

A)  0.652 
B)  2.12 
C)  2.24 
D)  2.77 
E)  2.90 
A)  0.652 
B)  2.12 
C)  2.24 
D)  2.77 
E)  2.90

Question 16

Two harmonic waves are described by     What is the wavelength of the resultant wave?

Accepted Answer

A)  3 m 
B)  2 m 
C)  1 m 
D)  4 m 
E)  6 m 
A)  3 m 
B)  2 m 
C)  1 m 
D)  4 m 
E)  6 m

Question 17

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−3 kg/m and a tension of 80 N when both ends are fixed in place.

Accepted Answer

100 Hz, 20

Question 18

The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women's voices. When we calculate the wavelength, we find that it is

Accepted Answer

A)  much shorter than the length of either a man's or woman's lips. 
B)  shorter than the length of a man's lips, but about the length of a woman's lips. 
C)  longer than a woman's lips, but about the length of a man's lips. 
D)  much longer than the length of either a man's or a woman's lips. 
E)  about the same length as either a man's or woman's lips. 
A)  much shorter than the length of either a man's or woman's lips. 
B)  shorter than the length of a man's lips, but about the length of a woman's lips. 
C)  longer than a woman's lips, but about the length of a man's lips. 
D)  much longer than the length of either a man's or a woman's lips. 
E)  about the same length as either a man's or woman's lips.

Question 19

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?

Accepted Answer

A)  3.4 
B)  172 
C)  344 
D)  1.7 
E)  688 
A)  3.4 
B)  172 
C)  344 
D)  1.7 
E)  688

Question 20

Two harmonic waves are described by     What is the frequency (in Hz) of the resultant wave?

Accepted Answer

A)  300 
B)  48 
C)  8 
D)  0.8 
E)  150 
A)  300 
B)  48 
C)  8 
D)  0.8 
E)  150

Exam 18: Superposition and Standing Waves

The path difference between two waves is 5m. If the wavelength of the waves emitted by the two sources is 4m, what is the phase difference (in degrees)?

If a supersonic plane is flying at increasing speed as the temperature decreases, what happens to the Mach number in this instance?

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

Two waves are described by y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters). With what angular frequency does the maximum amplitude of the resultant wave vary with time?

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

As shown below, a garden room has three walls, a floor and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is

Two harmonic waves are described by From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

A source of sound waves is placed at the center of a very large sound-reflecting wall. The source emits 0.500 W of power. Two meters from the source the intensity in W/m2 is

The superposition of two waves, and , results in a wave with a phase angle of

Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

The intensity level of an orchestra is 85 dB. A single violin achieves a level of 70 dB. How does the intensity of the sound of the full orchestra compare with that of the violin?

Two harmonic waves are described by What is the wavelength of the resultant wave?

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−3 kg/m and a tension of 80 N when both ends are fixed in place.

The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women's voices. When we calculate the wavelength, we find that it is

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?

Two harmonic waves are described by What is the frequency (in Hz) of the resultant wave?

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Two waves are described by y₁ = 6 cos 180t and y₂ = 6 cos 186t, (both in meters). With what angular frequency does the maximum amplitude of the resultant wave vary with time?

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (f_c = 261.6 Hz)?

A source of sound waves is placed at the center of a very large sound-reflecting wall. The source emits 0.500 W of power. Two meters from the source the intensity in W/m² is

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−³ kg/m and a tension of 80 N when both ends are fixed in place.