Question 1

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.

Question 2

Two sound waves,one wave is given by y1 = po sin ($\omega$1t),and the other by y2 = po sin ($\omega$2t),where $\omega$1 differs from $\omega$2 by a rad/s.The maximum sound intensity of the beat frequency is

Accepted Answer

A) po2 
B) 2po2 
C) 4po2 
D) 8po2 
E)  0

Question 3

A 1.00 m string fixed at both ends vibrates in its fundamental mode at 440 Hz.What is the speed of the waves on this string?

Accepted Answer

A) 220 m/s 
B) 440 m/s 
C) 660 m/s 
D) 880 m/s 
E) 1.10 km/s

Question 4

Middle C on a piano has a frequency of 262 Hz.Sometimes it is said that middle C is actually 28 = 256 Hz,and tuning forks are made with this frequency.How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned)piano?

Accepted Answer

A) 3 
B) 6 
C) 12 
D) 4 
E) 8

Question 5

Sound has a velocity of 335 m/s in air.For an air column that is closed at both ends to resonate to a frequency of 528 Hz,the length of the air column could be

Accepted Answer

A) 79.2 cm 
B) 55.5 cm 
C) 47.5 cm 
D) 31.7 cm 
E) 15.8 cm

Question 6

If two identical waves with a phase difference of 3$\pi$ are added,the result is

Accepted Answer

A) a wave with the same frequency but twice the amplitude. 
B) a wave with the same amplitude but twice the frequency. 
C) a wave with zero amplitude. 
D) a wave with an intensity equal to the sum of the intensities of the two waves. 
E) This problem cannot be solved without knowing the wavelengths of the two waves.

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.

Question 8

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

Question 9

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.

Question 10

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s.The minimum distance between two points with a phase difference of 60º is

Accepted Answer

A) 0.040 m 
B) 0.12 m 
C) 0.14 m 
D) 0.24 m 
E) 25 m

Question 11

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

Accepted Answer

A) 7.65 cm 
B) 15.3 cm 
C) 23.0 cm 
D) 30.6 cm 
E) 53.6 cm

Question 12

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 amplitudes of the traveling wave that result in this standing wave are

Accepted Answer

A) 0.04 m 
B) 0.08 m 
C) 0.02 m 
D) 0.16 m 
E) impossible to tell given this information about the standing wave.

Question 13

The ratio of the fundamental frequency (first harmonic)of an open pipe to that of a closed pipe of the same length is

Accepted Answer

A) 2:1 
B) 7:8 
C) 4:5 
D) 3:2 
E) 1:2

Question 14

The fundamental frequency of a vibrating string is f1.If the tension in the string is increased by 50% while the linear density is held constant,the fundamental frequency becomes

Accepted Answer

A) f1  
B) 1.2f1  
C) 1.5f1  
D) 1.7f1  
E) 2f1

Question 15

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

Question 16

The standing waves on a string of length L that is fixed at both ends have a speed v.The three lowest frequencies of vibration are

Accepted Answer

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

Question 17

The fundamental frequency of a vibrating string is f1.If the tension in the string is doubled,the fundamental frequency becomes

Accepted Answer

A) f1/2 
B)    
C) f1  
D)   
E) 2f1

Question 18

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

Question 19

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

Accepted Answer

A) 12.9 cm 
B) 19.4 cm 
C) 25.8 cm 
D) 51.7 cm 
E) 194 cm

Question 20

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.To what harmonic does the 558 Hz resonance correspond?

Accepted Answer

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

Exam 16: Superposition and Standing Waves

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?

Two sound waves,one wave is given by y₁ = p_o sin ( $\omega$ ₁t) ,and the other by y₂ = p_o sin ( $\omega$ ₂t) ,where $\omega$ ₁ differs from $\omega$ ₂ by a rad/s.The maximum sound intensity of the beat frequency is

A 1.00 m string fixed at both ends vibrates in its fundamental mode at 440 Hz.What is the speed of the waves on this string?

Middle C on a piano has a frequency of 262 Hz.Sometimes it is said that middle C is actually 2⁸ = 256 Hz,and tuning forks are made with this frequency.How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano?

Sound has a velocity of 335 m/s in air.For an air column that is closed at both ends to resonate to a frequency of 528 Hz,the length of the air column could be

If two identical waves with a phase difference of 3 $\pi$ are added,the result is

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

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?

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

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s.The minimum distance between two points with a phase difference of 60º is

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

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 amplitudes of the traveling wave that result in this standing wave are

The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is

The fundamental frequency of a vibrating string is f₁.If the tension in the string is increased by 50% while the linear density is held constant,the fundamental frequency becomes

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

The standing waves on a string of length L that is fixed at both ends have a speed v.The three lowest frequencies of vibration are

The fundamental frequency of a vibrating string is f₁.If the tension in the string is doubled,the fundamental frequency becomes

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

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.To what harmonic does the 558 Hz resonance correspond?

Exam 16: Superposition and Standing Waves

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?

Two sound waves,one wave is given by y1 = po sin ( ω\omegaω 1t) ,and the other by y2 = po sin ( ω\omegaω 2t) ,where ω\omegaω 1 differs from ω\omegaω 2 by a rad/s.The maximum sound intensity of the beat frequency is

A 1.00 m string fixed at both ends vibrates in its fundamental mode at 440 Hz.What is the speed of the waves on this string?

Middle C on a piano has a frequency of 262 Hz.Sometimes it is said that middle C is actually 28 = 256 Hz,and tuning forks are made with this frequency.How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano?

Sound has a velocity of 335 m/s in air.For an air column that is closed at both ends to resonate to a frequency of 528 Hz,the length of the air column could be

If two identical waves with a phase difference of 3 π\piπ are added,the result is

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

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?

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

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s.The minimum distance between two points with a phase difference of 60º is

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

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 amplitudes of the traveling wave that result in this standing wave are

The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is

The fundamental frequency of a vibrating string is f1.If the tension in the string is increased by 50% while the linear density is held constant,the fundamental frequency becomes

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

The standing waves on a string of length L that is fixed at both ends have a speed v.The three lowest frequencies of vibration are

The fundamental frequency of a vibrating string is f1.If the tension in the string is doubled,the fundamental frequency becomes

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

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about

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.To what harmonic does the 558 Hz resonance correspond?

Two sound waves,one wave is given by y₁ = p_o sin ( $\omega$ ₁t) ,and the other by y₂ = p_o sin ( $\omega$ ₂t) ,where $\omega$ ₁ differs from $\omega$ ₂ by a rad/s.The maximum sound intensity of the beat frequency is

Middle C on a piano has a frequency of 262 Hz.Sometimes it is said that middle C is actually 2⁸ = 256 Hz,and tuning forks are made with this frequency.How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano?

If two identical waves with a phase difference of 3 $\pi$ are added,the result is

The fundamental frequency of a vibrating string is f₁.If the tension in the string is increased by 50% while the linear density is held constant,the fundamental frequency becomes

The fundamental frequency of a vibrating string is f₁.If the tension in the string is doubled,the fundamental frequency becomes