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Resonance tube experiment

utkarshakash

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1. Homework Statement
A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in air column were obtained by lowering the water level. The resonance with the shorter air column is the first resonance and that with the longer air column is the second resonance. Then choose correct options

A) The intensity of sound heard at the first resonance was more than that at the second resonance.
B)the prongs of the tuning fork were kept in a horizontal plane above the resonance tube.
C)the amplitude of vibration of the ends of the prongs is typically around 1cm.
D)the length of the air column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.


3. The Attempt at a Solution

If I consider first option, I don't think it is correct as the intensity will not change. In both cases resonance occurs. So it should be same. option B) is incorrect as it is kept in vertical plane. I have no idea about C). The difference in length of two air columns should be λ/2. But from this I cannot make out about length of first air column.
 

haruspex

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If I consider first option, I don't think it is correct as the intensity will not change. In both cases resonance occurs. So it should be same.
Seems reasonable.
option B) is incorrect as it is kept in vertical plane.
Right.
I have no idea about C).
Roughly how far apart are the prongs (at rest)? Could they oscillate by 1cm?
The difference in length of two air columns should be λ/2. But from this I cannot make out about length of first air column.
What is the arrangement of nodes and antinodes at the first resonance?
 

utkarshakash

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What is the arrangement of nodes and antinodes at the first resonance?
At first resonance antinode is present at the open end of the tube and node is present at the water column.
 

haruspex

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At first resonance antinode is present at the open end of the tube and node is present at the water column.
So what fraction of a wavelength does that represent?
 

utkarshakash

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So what fraction of a wavelength does that represent?
It should be λ/4.
 

haruspex

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It should be λ/4.
Right. So the question is, is there some reason that it would be "somewhat shorter" than that.
I can't think of one, but I might be missing something. Check your course notes.
 

utkarshakash

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Right. So the question is, is there some reason that it would be "somewhat shorter" than that.
I can't think of one, but I might be missing something. Check your course notes.
Sometimes we also take in consideration the end correction. So it should be somewhat longer rather than shorter. The correct options according to answer key are A) and D).
 

haruspex

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Sometimes we also take in consideration the end correction. So it should be somewhat longer rather than shorter.
Are you sure you don't have that backwards? According to http://www.fonema.se/mouthcorr/mouthcorr.htm, "the pipe appears to be acoustically somewhat longer than its physical length". That means the physical length will be less then a quarter wavelength.
 

utkarshakash

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