Question 1

Which of the following wavelengths could NOT be present as a standing wave in a 2 m long organ pipe open at both ends?

Accepted Answer

A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m 
A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m

Question 2

Transverse waves y1 = A1 sin(k1x − ω1t)and y2 = A2 sin(k2x − ω2t),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)    . 
E)    . 
A) A1 − A2. 
B) A2 − A1. 
C) A1 + A2. 
D)    . 
E)    .

Question 3

Two harmonic waves are described by  
 
What is the phase (in rad)of the resultant wave when x = t = 0?

Accepted Answer

A) 3 
B) 0 
C) 2 
D) 1 
E) 4 
A) 3 
B) 0 
C) 2 
D) 1 
E) 4

Question 4

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 5

The superposition of two waves,  
And  
,
Results in a wave with a frequency of

Accepted Answer

A) 85 Hz. 
B) 170 Hz. 
C) 85π Hz. 
D) 340 Hz. 
E) 170π Hz. 
A) 85 Hz. 
B) 170 Hz. 
C) 85π Hz. 
D) 340 Hz. 
E) 170π Hz.

Question 6

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 7

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 8

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

Question 9

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 10

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency.At the time,the speed of sound in air is 340 m/s.How many beats per second do the people on the fire engine hear?

Accepted Answer

A) 0 
B) 15 
C) 29 
D) 63 
E) 250 
A) 0 
B) 15 
C) 29 
D) 63 
E) 250

Question 11

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x)cos (3t)where x is in m and t is in s.What is the speed (in m/s)of the interfering waves?

Accepted Answer

A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0 
A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0

Question 12

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 13

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 14

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,200

Question 15

A string is stretched and fixed at both ends,200 cm apart.If the density of the string is 0.015 g/cm,and its tension is 600 N,what is the wavelength (in cm)of the first harmonic?

Accepted Answer

A) 600 
B) 400 
C) 800 
D) 1 000 
E) 200 
A) 600 
B) 400 
C) 800 
D) 1 000 
E) 200

Question 16

Two harmonic waves are described by  
 
What is the magnitude of the displacement (in cm)of this wave at x = 3 cm and t = 5 sec?

Accepted Answer

A) 12.0 
B) 3.00 
C) 6.00 
D) 2.25 
E) 0 
A) 12.0 
B) 3.00 
C) 6.00 
D) 2.25 
E) 0

Question 17

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)    . 
B)    . 
C)    . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A. 
A)    . 
B)    . 
C)    . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A.

Question 18

A length of organ pipe is closed at one end.If the speed of sound is 344 m/s,what length of pipe (in cm)is needed to obtain a fundamental frequency of 50 Hz?

Accepted Answer

A) 28 
B) 86 
C) 344 
D) 172 
E) 688 
A) 28 
B) 86 
C) 344 
D) 172 
E) 688

Question 19

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 20

A string with a fixed frequency vibrator at one end is subjected to varying tensions.When the tension is 20 N,a resonance with 3 antinodes results.What tension would cause a resonance with 2 antinodes in this string?

Accepted Answer

A) 30 N 
B) 45 N 
C) 80 N 
D) 8.9 N 
E) 13 N 
A) 30 N 
B) 45 N 
C) 80 N 
D) 8.9 N 
E) 13 N

Exam 18: Superposition and Standing Waves

Which of the following wavelengths could NOT be present as a standing wave in a 2 m long organ pipe open at both ends?

Transverse waves y1 = A1 sin(k1x − ω1t)and y2 = A2 sin(k2x − ω2t),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

Two harmonic waves are described by What is the phase (in rad)of the resultant wave when x = t = 0?

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

The superposition of two waves, And , Results in a wave with a frequency of

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)?

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

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

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?

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency.At the time,the speed of sound in air is 340 m/s.How many beats per second do the people on the fire engine hear?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x)cos (3t)where x is in m and t is in s.What is the speed (in m/s)of the interfering waves?

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.

A string is stretched and fixed at both ends,200 cm apart.If the density of the string is 0.015 g/cm,and its tension is 600 N,what is the wavelength (in cm)of the first harmonic?

Two harmonic waves are described by What is the magnitude of the displacement (in cm)of this wave at x = 3 cm and t = 5 sec?

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 length of organ pipe is closed at one end.If the speed of sound is 344 m/s,what length of pipe (in cm)is needed to obtain a fundamental frequency of 50 Hz?

The superposition of two waves, And , Results in a wave with a phase angle of

A string with a fixed frequency vibrator at one end is subjected to varying tensions.When the tension is 20 N,a resonance with 3 antinodes results.What tension would cause a resonance with 2 antinodes in this string?

Physics and Measurement

Motion in One Dimension

Vectors

Motion in Two Dimensions

The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

Angular Momentum

Static Equilibrium and Elasticity

Universal Gravitation

Fluid Mechanics

Oscillatory Motion

Wave Motion

Sound Waves

Temperature

The First Law of Thermodynamics

The Kinetic Theory of Gases

Heat Engines, entropy, and the Second Law of Thermodynamics

Electric Fields

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Sources of the Magnetic Field

Faradays Law

Inductance

Alternating-Current Circuits

Electromagnetic Waves

The Nature of Light and the Principles of Ray Optics

Image Formation

Wave Optics

Diffraction Patterns and Polarization

Relativity

Introduction to Quantum Physics

Quantum Mechanics

Atomic Physics

Molecules and Solids

Nuclear Structure

Applications of Nuclear Physics

Particle Physics and Cosmology

Filters

Transverse waves y₁ = A₁ sin(k₁x − ω₁t)and y₂ = A₂ sin(k₂x − ω₂t),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

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)?

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.