Question 1

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)    C

Question 2

The superposition of two waves, $$y _ { 1 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t \right) \right]$$ and $$y _ { 2 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t - \frac { 1 } { 2 } \right) \right]$$ , results in a wave with a wavelength of

Accepted Answer

A)  $\frac { \pi } { 2 }$ m. 
B) 2 m. 
C)  $\pi$  m. 
D) 4 m. 
E) 4 $\pi$ m. 
A)  $\frac { \pi } { 2 }$ m. 
B) 2 m. 
C)  $\pi$  m. 
D) 4 m. 
E) 4 $\pi$ m. D

Question 3

Two harmonic waves are described by $$y _ { 1 } = ( 3 \mathrm {~cm} ) \sin \left( \frac { 8.0 } { \mathrm {~m} } x + \frac { 2.0 } { \mathrm {~s} } t \right)$$ $$y _ { 2 } = ( 3 \mathrm {~cm} ) \sin \left( \frac { 8.0 } { m } x - \frac { 2.0 } { \mathrm {~s} } t \right)$$ What is the magnitude of the speed (in m/s)of the two traveling waves?

Accepted Answer

A) 16 
B) 4.0 
C) 8.0 
D) 0.25 
E) 2.0 
A) 16 
B) 4.0 
C) 8.0 
D) 0.25 
E) 2.0 D

Question 4

Two harmonic waves are described by $y _ { 1 } = ( 6 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 8 } { \mathrm {~m} } x + \frac { 2 } { \mathrm {~s} } t \right) \right)$
$$y _ { 2 } = ( 6 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 8 } { \mathrm {~m} } x - \frac { 2 } { \mathrm {~s} } t \right) \right)$$ 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 5

In a standing wave,not necessarily at the fundamental frequency,on a string of length L,the distance between nodes is

Accepted Answer

A) $\lambda$/4. 
B) $\lambda$/2. 
C) $\lambda$. 
D) L/4. 
E) L/2. 
A) $\lambda$/4. 
B) $\lambda$/2. 
C) $\lambda$. 
D) L/4. 
E) L/2.

Question 6

When two organ pipes each closed at one end 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 7

Transverse waves y1 = A1 sin(k1x - $ \omega $1t)and y2 = A2 sin(k2x -  $ \omega $2t),with A2 > A1,start at opposite ends of a long rope when t = 0.The magnitude of the maximum displacement,y,of the rope at any point is

Accepted Answer

A) A1- A2. 
B) A2- A1. 
C) A1 + A2. 
D)  $\left( A _ { 1 } - A _ { 2 } \right) \frac { k _ { 1 } } { k _ { 2 } }$ . 
E)  $\left( A _ { 2 } - A _ { 1 } \right) \frac { k _ { 2 } } { k _ { 1 } }$ . 
A) A1- A2. 
B) A2- A1. 
C) A1 + A2. 
D)  $\left( A _ { 1 } - A _ { 2 } \right) \frac { k _ { 1 } } { k _ { 2 } }$ . 
E)  $\left( A _ { 2 } - A _ { 1 } \right) \frac { k _ { 2 } } { k _ { 1 } }$ .

Question 8

The figure below shows the positions of particles in a longitudinal standing wave.One quarter period later the particle distribution is shown in

Accepted Answer

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

Question 9

Tuning forks #1,#2,and #3 each have slightly different frequencies.When #1 and #2 are sounded together,a beat frequency of 3 Hz results.When #2 and #3 are sounded together,a beat frequency of 5 Hz results.If the frequency of #1 is 100 Hz,which of the following cannot be the frequency of #3?

Accepted Answer

A) 92 Hz 
B) 95 Hz 
C) 98 Hz 
D) 102 Hz 
E) 108 Hz 
A) 92 Hz 
B) 95 Hz 
C) 98 Hz 
D) 102 Hz 
E) 108 Hz

Question 10

Two identical strings have the same length and same mass per unit length.String B is stretched with four times as great a tension as that applied to string A.Which statement is correct for all n harmonics on the two strings,n = 1,2,3...?

Accepted Answer

A)  $f _ { \mathrm { nb } } = \frac { 1 } { 4 } f _ { \mathrm { nA } }$ . 
B)  $f _ { \mathrm { nb } } = \frac { 1 } { 2 } f _ { \mathrm { nA } }$ . 
C)  $f _ { n , B } = \sqrt { 2 } f _ { n , A }$ . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A. 
A)  $f _ { \mathrm { nb } } = \frac { 1 } { 4 } f _ { \mathrm { nA } }$ . 
B)  $f _ { \mathrm { nb } } = \frac { 1 } { 2 } f _ { \mathrm { nA } }$ . 
C)  $f _ { n , B } = \sqrt { 2 } f _ { n , A }$ . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A.

Question 11

A clarinet behaves like a tube closed at one end.If its length is 1.0 m,and the velocity of sound is 344 m/s,what is its fundamental frequency (in Hz)?

Accepted Answer

A) 264 
B) 140 
C) 86 
D) 440 
E) 172 
A) 264 
B) 140 
C) 86 
D) 440 
E) 172

Question 12

Two harmonic waves are described by $$y _ { 1 } = ( 4 \mathrm {~m} ) \sin \left( \frac { 8 } { m } x - \frac { 300 } { \mathrm {~s} } t \right)$$ $$y _ { 2 } = ( 4 m ) \sin \left( \frac { 8 } { m } x - \frac { 300 } { s } t - 2 \right)$$ 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

Question 13

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x)cos (6t)where x is in m and t is in s.What is the approximate frequency of the interfering waves?

Accepted Answer

A) 3 Hz 
B) 1 Hz 
C) 6 Hz 
D) 12 Hz 
E) 5 Hz 
A) 3 Hz 
B) 1 Hz 
C) 6 Hz 
D) 12 Hz 
E) 5 Hz

Question 14

Two speakers in an automobile emit sound waves that are in phase at the speakers.One speaker is 40 cm ahead of and 30 cm to the left of the driver's left ear.The other speaker is 50 cm ahead of and 120 cm to the right of the driver's right ear.Which of the following wavelengths is(are)in phase at the left ear for the speaker on the left and the right ear for the speaker on the right?

Accepted Answer

A) 10 cm 
B) 20 cm 
C) 650 cm 
D) All of the wavelengths listed above. 
E) Only the wavelengths listed in (a)and (b). 
A) 10 cm 
B) 20 cm 
C) 650 cm 
D) All of the wavelengths listed above. 
E) Only the wavelengths listed in (a)and (b).

Question 15

Two instruments produce a beat frequency of 5 Hz.If one has a frequency of 264 Hz,what could be the frequency of the other instrument?

Accepted Answer

A) 269 Hz 
B) 254 Hz 
C) 264 Hz 
D) 5 Hz 
E) 274 Hz 
A) 269 Hz 
B) 254 Hz 
C) 264 Hz 
D) 5 Hz 
E) 274 Hz

Question 16

Superposition of waves can occur

Accepted Answer

A) in transverse waves. 
B) in longitudinal waves. 
C) in sinusoidal waves. 
D) in all of the above. 
E) only in (a)and (c)above. 
A) in transverse waves. 
B) in longitudinal waves. 
C) in sinusoidal waves. 
D) in all of the above. 
E) only in (a)and (c)above.

Question 17

An observer stands 3 m from speaker A and 4 m from speaker B.Both speakers,oscillating in phase,produce 170 Hz waves.The speed of sound in air is 340 m/s.What is the phase difference (in radians)between the waves from A and B at the observer's location,point P?

Accepted Answer

A) 0 
B)  $\frac { \pi } { 2 }$ 
C)  $\pi$ 
D) 2 $\pi$ 
E) 4 $\pi$ 
A) 0 
B)  $\frac { \pi } { 2 }$ 
C)  $\pi$ 
D) 2 $\pi$ 
E) 4 $\pi$

Question 18

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator.Which of the following can be changed by changing the frequency of the oscillator?

Accepted Answer

A) The speed of the waves traveling along the string. 
B) The tension in the string. 
C) The wavelength of the waves on the string. 
D) All of the above. 
E) None of the above. 
A) The speed of the waves traveling along the string. 
B) The tension in the string. 
C) The wavelength of the waves on the string. 
D) All of the above. 
E) None of the above.

Question 19

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

Question 20

Two tuning forks with frequencies 264 and 262 Hz produce "beats".What is the beat frequency (in Hz)?

Accepted Answer

A) 4 
B) 2 
C) 1 
D) 3 
E) 0 (no beats are produced) 
A) 4 
B) 2 
C) 1 
D) 3 
E) 0 (no beats are produced)

Exam 14: Superposition and Standing 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

In a standing wave,not necessarily at the fundamental frequency,on a string of length L,the distance between nodes is

When two organ pipes each closed at one end 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?

Transverse waves y1 = A1 sin(k1x - ω \omega ω 1t)and y2 = A2 sin(k2x - ω \omega ω 2t),with A2 > A1,start at opposite ends of a long rope when t = 0.The magnitude of the maximum displacement,y,of the rope at any point is

The figure below shows the positions of particles in a longitudinal standing wave.One quarter period later the particle distribution is shown in

Tuning forks #1,#2,and #3 each have slightly different frequencies.When #1 and #2 are sounded together,a beat frequency of 3 Hz results.When #2 and #3 are sounded together,a beat frequency of 5 Hz results.If the frequency of #1 is 100 Hz,which of the following cannot be the frequency of #3?

Two identical strings have the same length and same mass per unit length.String B is stretched with four times as great a tension as that applied to string A.Which statement is correct for all n harmonics on the two strings,n = 1,2,3...?

A clarinet behaves like a tube closed at one end.If its length is 1.0 m,and the velocity of sound is 344 m/s,what is its fundamental frequency (in Hz)?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x)cos (6t)where x is in m and t is in s.What is the approximate frequency of the interfering waves?

Two instruments produce a beat frequency of 5 Hz.If one has a frequency of 264 Hz,what could be the frequency of the other instrument?

Superposition of waves can occur

An observer stands 3 m from speaker A and 4 m from speaker B.Both speakers,oscillating in phase,produce 170 Hz waves.The speed of sound in air is 340 m/s.What is the phase difference (in radians)between the waves from A and B at the observer's location,point P?

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator.Which of the following can be changed by changing the frequency of the oscillator?

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)?

Two tuning forks with frequencies 264 and 262 Hz produce "beats".What is the beat frequency (in Hz)?

Introduction and Vectors

Motion in One Dimension

Motion in Two Dimensions

The Laws of Motion

More Applications of Newtons Laws

Energy of a System

Conservation of Energy

Momentum and Collisions

Relativity

Rotational Motion

Gravity,planetary Orbits,and the Hydrogen Atom

Oscillatory Motion

Mechanical Waves

Fluid Mechanics

Temperature and the Kinetic Theory of Gases

Energy in Thermal Processes: the First Law of Thermodynamics

Heat Engines,entropy,and the Second Law of Thermodynamics

Electric Forces and Electric Fields

Electric Potential and Capacitance

Current and Direct Current Circuits

Magnetic Forces and Magnetic Fields

Faradays Law and Inductance

Electromagnetic Waves

Reflection and Refraction of Light

Image Formation by Mirrors and Lenses

Wave Optics

Quantum Physics

Atomic Physics

Nuclear Physics

Particle Physics

Filters

Transverse waves y₁ = A₁ sin(k₁x - $\omega$ ₁t)and y₂ = A₂ sin(k₂x - $\omega$ ₂t),with A₂ > A₁,start at opposite ends of a long rope when t = 0.The magnitude of the maximum displacement,y,of the rope at any point is