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Exam 17: Superposition

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Question 1

Multiple Choice

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The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz.Which one of the following frequencies will NOT resonate in the same pipe?

A) 400 Hz
B) 600 Hz
C) 800 Hz
D) 900 Hz
E) 1000 Hz

F) B) and E)
G) C) and E)

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Question 2

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A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends.In its third harmonic it vibrates at 512 Hz.The density of platinum is 21.4 × 10³ kg/m³.What is the tension in the wire?

A) 4.00 kN
B) 2.00 kN
C) 2.82 kN
D) 1.41 kN
E) 1.00 kN

F) A) and B)
G) A) and E)

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C

Question 3

Multiple Choice

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Consider a pipe of length L that is open at both ends.What are the wavelengths of the three lowest-pitch tones produced by this pipe?

Two pure tones are sounded together and a particular beat frequency is heard.What happens to the beat frequency if the frequency of one of the tones is increased?

A string 40.0 cm long of mass 8.50 g is fixed at both ends and is under a tension of 425 N.When this string is vibrating in its third OVERTONE,you observe that it causes a nearby pipe,open at both ends,to resonate in its third HARMONIC.The speed of sound in the room is 344 m/s. (a)How long is the pipe? (b)What is the fundamental frequency of the pipe?

Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz.The speed of sound in the room is 344 m/s.If you start out standing midway between the speakers,find the shortest distance you can walk toward either speaker in order to hear a minimum of sound.

Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator whose frequency range is to A point P is located from one loudspeaker and 3.6 m from the other.The speed of sound is 344 m/s.The frequency produced by the oscillator,for which constructive interference of sound occurs at point P,is closest to

Two in-phase loudspeakers are some distance apart.They emit sound with a frequency of 1536 Hz.You move between the speakers,along the line joining them,at a constant speed of 2.8 m/s.What beat frequency do you observe? The speed of sound in the room is 330 m/s.

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m.A person is standing 12.0 m away from the wall,equidistant from the loudspeakers.When the person moves 1.00 m parallel to the wall,she experiences destructive interference for the first time.What is the frequency of the sound? The speed of sound in air is .

In a resonating pipe that is open at one end and closed at the other end,there

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long.When you gently pluck the upper end of the wire,a pulse travels down the wire and returns 7.84 ms later,having reflected off the lower end.The speed of sound in the room is 344 m/s,and the stone is heavy enough to prevent the lower end of the wire from moving.If the wire is vibrating in its second overtone,what is the frequency of the sound it will produce?

A 2.0-m string is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter.The carousel rotates with an angular velocity of 0.800 rad/s.A stationary listener is located at a distance from the carousel.The speed of sound is 350 m/s.The longest wavelength reaching the listener from the sirens is closest to

Two violinists are trying to tune their instruments in an orchestra.One is producing the desired frequency of 440.0 Hz.The other is producing a frequency of 448.4 Hz.By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long.When you gently pluck the upper end of the wire,a pulse travels down the wire and returns 7.84 ms later,having reflected off the lower end.The speed of sound in the room is 344 m/s,and the stone is heavy enough to prevent the lower end of the wire from moving.If the wire is vibrating in its second overtone,what is the wavelength of the sound it will produce?

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m.A person is standing 12.0 m away from the wall,equidistant from the loudspeakers.When the person moves 3.00 m parallel to the wall,she experiences destructive interference for the second time.What is the frequency of the sound? The speed of sound in the room is 343 m/s.CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers.

Two stereo speakers mounted 4.52 m apart on a wall emit identical in-phase sound waves.You are standing at the opposite wall of the room at a point directly between the two speakers.You walk 2.11 m parallel to the wall,to a location where you first notice that the sound intensity drops to zero.If the wall along which you are walking is 10.7 m from the wall with the speakers,what is the wavelength of the sound waves? CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers.

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz.If you now open the closed end,the fundamental frequency becomes

Two motors in a factory are running at slightly different rates.One runs at 825 rpm and the other at 786 rpm.You hear the sound intensity increase and then decrease periodically due to wave interference.How much time elapses between successive maxima of the sound intensity?