Question 1

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The frequency of the piano's A is

Accepted Answer

A)  440 Hz 
B)  444 Hz 
C)  880 Hz 
D)  436 Hz 
E)  either 436 Hz or 444 Hz 
A)  440 Hz 
B)  444 Hz 
C)  880 Hz 
D)  436 Hz 
E)  either 436 Hz or 444 Hz E

Question 2

Standing waves exist in a string of length L that is fixed at one end and free at the other. The speed of the waves on the string is v. The three lowest frequencies of vibration are

Accepted Answer

A)  v/4L, v/2L, and 3v/4L 
B)  v/2L, v/L, and 3v/2L 
C)  $\lambda$/4, $\lambda$/2, and 3$\lambda$/4 
D)  v/4L, 3v/4L, and 5v/4L 
E)  $\lambda$/3, 2$\lambda$/3, and 3$\lambda$/3 
A)  v/4L, v/2L, and 3v/4L 
B)  v/2L, v/L, and 3v/2L 
C)  $\lambda$/4, $\lambda$/2, and 3$\lambda$/4 
D)  v/4L, 3v/4L, and 5v/4L 
E)  $\lambda$/3, 2$\lambda$/3, and 3$\lambda$/3 D

Question 3

One wave moves to the right and a second wave (reflected) moves to the left to form a stationary wave. At which point(s) does the stationary wave have a node?

Accepted Answer

A)  1 
B)  3 and 5 
C)  2 
D)  4 and 6 
E)  2, 4, and 6 
A)  1 
B)  3 and 5 
C)  2 
D)  4 and 6 
E)  2, 4, and 6 D

Question 4

A stretched string of length L, fixed at both ends, is vibrating in its third harmonic. How far from the end of the string can the blade of a screwdriver be placed against the string without disturbing the amplitude of the vibration?

Accepted Answer

A)  L/6 
B)  L/4 
C)  L/5 
D)  L/2 
E)  None of these is correct. 
A)  L/6 
B)  L/4 
C)  L/5 
D)  L/2 
E)  None of these is correct.

Question 5

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 6

The figure shows a standing wave in a pipe that is closed at one end. The frequency associated with this wave pattern is called the

Accepted Answer

A)  first harmonic. 
B)  second harmonic. 
C)  third harmonic. 
D)  fourth harmonic. 
E)  fifth harmonic. 
A)  first harmonic. 
B)  second harmonic. 
C)  third harmonic. 
D)  fourth harmonic. 
E)  fifth harmonic.

Question 7

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The speed of the traveling waves that result in this standing wave is

Accepted Answer

A)  6.00 m 
B)  1.05 m 
C)  600 m 
D)  0.010 m 
E)  impossible to tell given this information about the standing wave. 
A)  6.00 m 
B)  1.05 m 
C)  600 m 
D)  0.010 m 
E)  impossible to tell given this information about the standing wave.

Question 8

Two loudspeakers S1 and S2, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener L directly in front of speaker  S1 notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). What is the lowest frequency of the emitted tone? The speed of sound in air is 340 m/s.

Accepted Answer

A)  85 Hz 
B)  0.17 kHz 
C)  0.26 kHz 
D)  0.34 kHz 
E)  0.51 kHz 
A)  85 Hz 
B)  0.17 kHz 
C)  0.26 kHz 
D)  0.34 kHz 
E)  0.51 kHz

Question 9

The third harmonic of a tube closed at one end is 735 Hz. If the speed of sound in air is 335 m/s, the length of the tube must be

Accepted Answer

A)  11.6 cm 
B)  22.9 cm 
C)  34.1 cm 
D)  45.7 cm 
E)  57.3 cm 
A)  11.6 cm 
B)  22.9 cm 
C)  34.1 cm 
D)  45.7 cm 
E)  57.3 cm

Question 10

Four pendulums are hung from a light rod that is free to rotate about its long axis. The pendulums have lengths L, 2L, L/2 and L, and masses m, m/2, 2m and 4m respectively. Pendulum 1 is set to swing at its natural frequency. Which of the other three will, over time, also oscillate at the same frequency?

Accepted Answer

A)  (2) 
B)  (3) 
C)  (4) 
D)  (2) and (3) 
E)  all three 
A)  (2) 
B)  (3) 
C)  (4) 
D)  (2) and (3) 
E)  all three

Question 11

A string of linear density $\mu$ and length L is under a constant tension T = mg. One end of the string is attached to a tunable harmonic oscillator. A resonant standing wave is observed

Accepted Answer

A)  at any frequency. 
B)  when the frequency   where n = 1, 2, 3, ... 
C)  when the frequency   where n = 1, 2, 3, ... 
D)  when the frequency   where n = 1, 2, 3, ...and vs is the speed of sound. 
E)  unable to tell 
A)  at any frequency. 
B)  when the frequency   where n = 1, 2, 3, ... 
C)  when the frequency   where n = 1, 2, 3, ... 
D)  when the frequency   where n = 1, 2, 3, ...and vs is the speed of sound. 
E)  unable to tell

Question 12

The complex wave whose frequency spectrum is shown in the figure is made up of waves whose frequencies are

Accepted Answer

A)  1, 2, and 4. 
B)  100, 200, and 400. 
C)  100, 100, and 400. 
D)  1 and 4. 
E)  100 and 400. 
A)  1, 2, and 4. 
B)  100, 200, and 400. 
C)  100, 100, and 400. 
D)  1 and 4. 
E)  100 and 400.

Question 13

The human vocal tract can be thought of as a tube that is open at one end. If the length of this tube is 17 cm (about average for an adult male), what are the lowest two harmonics?

Accepted Answer

A)  500 Hz, 1500 Hz 
B)  500 Hz, 1000 Hz 
C)  1000 Hz, 2000 Hz 
D)  1000 Hz, 3000 Hz 
E)  1500 Hz, 2500 Hz 
A)  500 Hz, 1500 Hz 
B)  500 Hz, 1000 Hz 
C)  1000 Hz, 2000 Hz 
D)  1000 Hz, 3000 Hz 
E)  1500 Hz, 2500 Hz

Question 14

Two wave trains travel on a string under a constant tension T. Which of the following statements is NOT correct?

Accepted Answer

A)  The two waves can have different speed. 
B)  The two waves can have different frequency. 
C)  The two waves can have different wavelength. 
D)  The superposition principle applies for the two waves. 
E)  At any point on the string, the resultant amplitude is the algebraic sum of the amplitudes of the two waves. 
A)  The two waves can have different speed. 
B)  The two waves can have different frequency. 
C)  The two waves can have different wavelength. 
D)  The superposition principle applies for the two waves. 
E)  At any point on the string, the resultant amplitude is the algebraic sum of the amplitudes of the two waves.

Question 15

A vibrating tuning fork of 725 Hz is held above a tube filled with water. Successive resonances are heard when the water level is lowered by 11.5 cm and 34.5 cm from the top of the tube. Calculate a value for the speed of sound. (Hint: remember the small end correction $\Delta$L at the top of the tube.)

Accepted Answer

A)  333 m/s 
B)  343 m/s 
C)  325 m/s 
D)  315 m/s 
E)  338 m/s 
A)  333 m/s 
B)  343 m/s 
C)  325 m/s 
D)  315 m/s 
E)  338 m/s

Question 16

A string with length L is fixed on both ends. If $\lambda$o = 2L and fo = v/$\lambda$0, the wave function for the harmonic shown is

Accepted Answer

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

Question 17

The fundamental frequency of a pipe that has one end closed is 256 Hz. When both ends of the same pipe are opened, the fundamental frequency is

Accepted Answer

A)  64.0 Hz 
B)  128 Hz 
C)  256 Hz 
D)  512 Hz 
E)  1.02 kHz 
A)  64.0 Hz 
B)  128 Hz 
C)  256 Hz 
D)  512 Hz 
E)  1.02 kHz

Question 18

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 19

Use the figure to the right to answer the next problems.
The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s.  
-The duration of the wave pulse is

Accepted Answer

A)  0.005 s 
B)  0.0005 s 
C)  0.001 s 
D)  0.02 s 
E)  0.5 s 
A)  0.005 s 
B)  0.0005 s 
C)  0.001 s 
D)  0.02 s 
E)  0.5 s

Question 20

Two sound waves, one wave is given by y1 = po sin (kx - $\omega$t) and the other by y2 = po sin (kx - $\omega$t + $\pi$/2). The amplitude resulting from the interference of the two waves is

Accepted Answer

A)  2po  
B)    
C)  1.25po  
D)    
E)  0 
A)  2po  
B)    
C)  1.25po  
D)    
E)  0

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The frequency of the piano's A is

Standing waves exist in a string of length L that is fixed at one end and free at the other. The speed of the waves on the string is v. The three lowest frequencies of vibration are

One wave moves to the right and a second wave (reflected) moves to the left to form a stationary wave. At which point(s) does the stationary wave have a node?

A stretched string of length L, fixed at both ends, is vibrating in its third harmonic. How far from the end of the string can the blade of a screwdriver be placed against the string without disturbing the amplitude of the vibration?

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

The figure shows a standing wave in a pipe that is closed at one end. The frequency associated with this wave pattern is called the

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The speed of the traveling waves that result in this standing wave is

The third harmonic of a tube closed at one end is 735 Hz. If the speed of sound in air is 335 m/s, the length of the tube must be

The complex wave whose frequency spectrum is shown in the figure is made up of waves whose frequencies are

The human vocal tract can be thought of as a tube that is open at one end. If the length of this tube is 17 cm (about average for an adult male), what are the lowest two harmonics?

Two wave trains travel on a string under a constant tension T. Which of the following statements is NOT correct?

The fundamental frequency of a pipe that has one end closed is 256 Hz. When both ends of the same pipe are opened, the fundamental frequency is

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in

Use the figure to the right to answer the next problems. The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s. -The duration of the wave pulse is

Two sound waves, one wave is given by y₁ = p_o sin (kx - $\omega$ t) and the other by y₂ = p_o sin (kx - $\omega$ t + $\pi$ /2). The amplitude resulting from the interference of the two waves is

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Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Conservation of Angular Momentum

Gravity

Static Equilibrium and Elasticity

Fluids

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Wave Motion

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The Second Law of Thermodynamics

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Exam 16: Superposition and Standing Waves

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The frequency of the piano's A is

Standing waves exist in a string of length L that is fixed at one end and free at the other. The speed of the waves on the string is v. The three lowest frequencies of vibration are

One wave moves to the right and a second wave (reflected) moves to the left to form a stationary wave. At which point(s) does the stationary wave have a node?

A stretched string of length L, fixed at both ends, is vibrating in its third harmonic. How far from the end of the string can the blade of a screwdriver be placed against the string without disturbing the amplitude of the vibration?

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

The figure shows a standing wave in a pipe that is closed at one end. The frequency associated with this wave pattern is called the

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The speed of the traveling waves that result in this standing wave is

The third harmonic of a tube closed at one end is 735 Hz. If the speed of sound in air is 335 m/s, the length of the tube must be

A string of linear density μ\muμ and length L is under a constant tension T = mg. One end of the string is attached to a tunable harmonic oscillator. A resonant standing wave is observed

The complex wave whose frequency spectrum is shown in the figure is made up of waves whose frequencies are

The human vocal tract can be thought of as a tube that is open at one end. If the length of this tube is 17 cm (about average for an adult male), what are the lowest two harmonics?

Two wave trains travel on a string under a constant tension T. Which of the following statements is NOT correct?

A string with length L is fixed on both ends. If λ\lambdaλ o = 2L and fo = v/ λ\lambdaλ 0, the wave function for the harmonic shown is

The fundamental frequency of a pipe that has one end closed is 256 Hz. When both ends of the same pipe are opened, the fundamental frequency is

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in

Use the figure to the right to answer the next problems. The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s. -The duration of the wave pulse is

Two sound waves, one wave is given by y1 = po sin (kx - ω\omegaω t) and the other by y2 = po sin (kx - ω\omegaω t + π\piπ /2). The amplitude resulting from the interference of the two waves is

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Conservation of Angular Momentum

Gravity

Static Equilibrium and Elasticity

Fluids

Oscillations

Wave Motion

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

Filters

Two sound waves, one wave is given by y₁ = p_o sin (kx - $\omega$ t) and the other by y₂ = p_o sin (kx - $\omega$ t + $\pi$ /2). The amplitude resulting from the interference of the two waves is