Question 1

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is

Accepted Answer

A)  $\pi$ radians. 
B)  $\pi$/2 radians. 
C)  $\pi$/4 radians. 
D)  $\pi$/8 radians. 
E)  $\pi$/16 radians. 
A)  $\pi$ radians. 
B)  $\pi$/2 radians. 
C)  $\pi$/4 radians. 
D)  $\pi$/8 radians. 
E)  $\pi$/16 radians.

Question 2

The reason we can tell the difference between a trumpet and a clarinet when they both play the same pitch is that they have

Accepted Answer

A)  the same overtones. 
B)  the same harmonics. 
C)  different fundamental frequencies. 
D)  different waveforms. 
E)  harmonic syntheses. 
A)  the same overtones. 
B)  the same harmonics. 
C)  different fundamental frequencies. 
D)  different waveforms. 
E)  harmonic syntheses.

Question 3

In graph A, two waves are shown at a given instant. What is the number of the curve in graph B that represents the wave resulting from the superposition of the two waves in A at this instant?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  The resultant is zero for all values of x. 
E)  None of these represent the wave. 
A)  1 
B)  2 
C)  3 
D)  The resultant is zero for all values of x. 
E)  None of these represent the wave.

Question 4

The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v. The frequencies of the three lowest harmonics 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

Question 5

At P2 the waves from sources S1 and S2 shown in the figure

Accepted Answer

A)  are in phase. 
B)  have a path difference of one wavelength. 
C)  have a path difference of one-half wavelength. 
D)  are interfering constructively. 
E)  None of these is correct. 
A)  are in phase. 
B)  have a path difference of one wavelength. 
C)  have a path difference of one-half wavelength. 
D)  are interfering constructively. 
E)  None of these is correct.

Question 6

A stretched string is fixed at points 1 and 5. When it is vibrating at the second harmonic frequency, the nodes of the standing wave are at points

Accepted Answer

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

Question 7

An examination of this frequency spectrum allows you to conclude that

Accepted Answer

A)  the odd harmonics 1 through 19 are present in the composite wave. 
B)  the even harmonics 2 through 20 are present in the composite wave. 
C)  the amplitudes of the component waves are equal. 
D)  the wave form is a simple sinusoid. 
E)  None of these is correct. 
A)  the odd harmonics 1 through 19 are present in the composite wave. 
B)  the even harmonics 2 through 20 are present in the composite wave. 
C)  the amplitudes of the component waves are equal. 
D)  the wave form is a simple sinusoid. 
E)  None of these is correct.

Question 8

A string is connected to a tuning fork whose frequency is 80.0 Hz and is held under tension by 0.500 kg. The tuning fork causes the string to vibrate as shown. The mass per unit length for the string is

Accepted Answer

A)  9.45 $\times$ 10-4 kg/m 
B)  6.80 $\times$ 10-3 kg/m 
C)  4.34 kg/m 
D)  6.00 $\times$ 10-3 kg/m 
E)  3.85 $\times$ 10-2 kg/m 
A)  9.45 $\times$ 10-4 kg/m 
B)  6.80 $\times$ 10-3 kg/m 
C)  4.34 kg/m 
D)  6.00 $\times$ 10-3 kg/m 
E)  3.85 $\times$ 10-2 kg/m

Question 9

If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by

Accepted Answer

A)  1 
B)  2 
C)    
D)    
E)    
A)  1 
B)  2 
C)    
D)    
E)

Question 10

A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies. The amplitude of the antinodes is very much larger than the amplitude of the oscillator. Does this violate the conservation of energy principle? Explain why.

Accepted Answer

A)  Yes, since E is proportional to amplitude squared. 
B)  Yes, since there is large kinetic energy of the string, and this is much bigger than the energy from the oscillator. 
C)  No, energy from waves does not obey the conservation of energy principle in the first place. 
D)  No, the energy at the antinodes builds up after the first few cycles, after which the dissipation due to friction equals the energy supplied by the oscillator. 
E)  Whether it obeys the conservation of energy principle depends on the tension in the string. 
A)  Yes, since E is proportional to amplitude squared. 
B)  Yes, since there is large kinetic energy of the string, and this is much bigger than the energy from the oscillator. 
C)  No, energy from waves does not obey the conservation of energy principle in the first place. 
D)  No, the energy at the antinodes builds up after the first few cycles, after which the dissipation due to friction equals the energy supplied by the oscillator. 
E)  Whether it obeys the conservation of energy principle depends on the tension in the string.

Question 11

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the fundamental frequency of the string?

Accepted Answer

A)  558 Hz 
B)  372 Hz 
C)  93 Hz 
D)  186 Hz 
E)  none of the above 
A)  558 Hz 
B)  372 Hz 
C)  93 Hz 
D)  186 Hz 
E)  none of the above

Question 12

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

Accepted Answer

A)  2.0 mm 
B)  1.8 mm 
C)  1.4 mm 
D)  1.0 mm 
E)  zero 
A)  2.0 mm 
B)  1.8 mm 
C)  1.4 mm 
D)  1.0 mm 
E)  zero

Question 13

The sound wave in an organ tube has a wavelength that is equal to the distance between

Accepted Answer

A)  A and B. 
B)  A and C. 
C)  the nodes farthest apart. 
D)  the antinodes farthest apart. 
E)  None of these is correct. 
A)  A and B. 
B)  A and C. 
C)  the nodes farthest apart. 
D)  the antinodes farthest apart. 
E)  None of these is correct.

Question 14

Use the figure to the right to answer the next problems.
The graph shows three harmonics.  
-The frequency spectrum of the composite wave is best represented by

Accepted Answer

A)  
  
B)  
  
C)  
  
D)    
E)  None of the above 
A)  
  
B)  
  
C)  
  
D)    
E)  None of the above

Question 15

The fundamental frequency of a vibrating string is   . If the tension in the string is quadrupled while the linear density is held constant, the fundamental frequency becomes

Accepted Answer

A)    
B)  1.  
C)  1.  
D)  1.  
E)    
A)    
B)  1.  
C)  1.  
D)  1.  
E)

Question 16

On a standing-wave pattern, the distance between two consecutive nodes is d. The wavelength is

Accepted Answer

A)  d/2 
B)  d 
C)  3d/2 
D)  2d 
E)  4d 
A)  d/2 
B)  d 
C)  3d/2 
D)  2d 
E)  4d

Question 17

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to

Accepted Answer

A)  1.0 radians. 
B)  1.5 radians. 
C)  2.0 radians. 
D)  2.5 radians. 
E)  3.0 radians. 
A)  1.0 radians. 
B)  1.5 radians. 
C)  2.0 radians. 
D)  2.5 radians. 
E)  3.0 radians.

Question 18

Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.

Accepted Answer

A)  256 Hz 
B)  1024 Hz 
C)  512 Hz 
D)  341 Hz 
E)  683 Hz 
A)  256 Hz 
B)  1024 Hz 
C)  512 Hz 
D)  341 Hz 
E)  683 Hz

Question 19

The electronic music synthesizer is based on the results of

Accepted Answer

A)  harmonic synthesis. 
B)  overtones. 
C)  tone quality. 
D)  Fourier analysis. 
E)  all of these factors. 
A)  harmonic synthesis. 
B)  overtones. 
C)  tone quality. 
D)  Fourier analysis. 
E)  all of these factors.

Question 20

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 wavelength of this 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.

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is

The reason we can tell the difference between a trumpet and a clarinet when they both play the same pitch is that they have

In graph A, two waves are shown at a given instant. What is the number of the curve in graph B that represents the wave resulting from the superposition of the two waves in A at this instant?

The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v. The frequencies of the three lowest harmonics are

At P₂ the waves from sources S₁ and S₂ shown in the figure

A stretched string is fixed at points 1 and 5. When it is vibrating at the second harmonic frequency, the nodes of the standing wave are at points

An examination of this frequency spectrum allows you to conclude that

A string is connected to a tuning fork whose frequency is 80.0 Hz and is held under tension by 0.500 kg. The tuning fork causes the string to vibrate as shown. The mass per unit length for the string is

If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by

A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies. The amplitude of the antinodes is very much larger than the amplitude of the oscillator. Does this violate the conservation of energy principle? Explain why.

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the fundamental frequency of the string?

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

The sound wave in an organ tube has a wavelength that is equal to the distance between

Use the figure to the right to answer the next problems. The graph shows three harmonics. -The frequency spectrum of the composite wave is best represented by

The fundamental frequency of a vibrating string is . If the tension in the string is quadrupled while the linear density is held constant, the fundamental frequency becomes

On a standing-wave pattern, the distance between two consecutive nodes is d. The wavelength is

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to

Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.

The electronic music synthesizer is based on the results of

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 wavelength of this wave 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

Exam 16: Superposition and Standing Waves

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is

The reason we can tell the difference between a trumpet and a clarinet when they both play the same pitch is that they have

In graph A, two waves are shown at a given instant. What is the number of the curve in graph B that represents the wave resulting from the superposition of the two waves in A at this instant?

The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v. The frequencies of the three lowest harmonics are

At P2 the waves from sources S1 and S2 shown in the figure

A stretched string is fixed at points 1 and 5. When it is vibrating at the second harmonic frequency, the nodes of the standing wave are at points

An examination of this frequency spectrum allows you to conclude that

A string is connected to a tuning fork whose frequency is 80.0 Hz and is held under tension by 0.500 kg. The tuning fork causes the string to vibrate as shown. The mass per unit length for the string is

If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by

A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies. The amplitude of the antinodes is very much larger than the amplitude of the oscillator. Does this violate the conservation of energy principle? Explain why.

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the fundamental frequency of the string?

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

The sound wave in an organ tube has a wavelength that is equal to the distance between

Use the figure to the right to answer the next problems. The graph shows three harmonics. -The frequency spectrum of the composite wave is best represented by

The fundamental frequency of a vibrating string is . If the tension in the string is quadrupled while the linear density is held constant, the fundamental frequency becomes

On a standing-wave pattern, the distance between two consecutive nodes is d. The wavelength is

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to

Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.

The electronic music synthesizer is based on the results of

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 wavelength of this wave 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

At P₂ the waves from sources S₁ and S₂ shown in the figure