Frequency of vibration of air column

[Amith2006]

Sir,
Consider a resonance column which is in unison with a tuning fork of particular frequency. Now by varying the length of the air column, resonance is obtained at different lengths. How is this possible? I have this doubt because each length of air column vibrates with a particular frequency. So when the length of air column is changed, the frequency also changes isn’t it? My question is even after the change in frequency, how is resonance obtained by using the tuning fork of same frequency?

 

[Andrew Mason]

Sir,
Consider a resonance column which is in unison with a tuning fork of particular frequency. Now by varying the length of the air column, resonance is obtained at different lengths. How is this possible? I have this doubt because each length of air column vibrates with a particular frequency. So when the length of air column is changed, the frequency also changes isn’t it? My question is even after the change in frequency, how is resonance obtained by using the tuning fork of same frequency?

What frequencies, other than the tuning fork fundamental frequency, will the tuning fork resonate with? What is the definition of resonance?

AM

 

[Amith2006]

Sir,
I know that a tuning fork will vibrate only with a single frequency and resonance takes place when the frequency of the tuning fork becomes equal to the fundamental frequency of vibration of the air column. But in a resonance column we speak about first resonance say for 48cm length of air column. Suppose some water is poured into the resonance tube until resonance is obtained at another length say 24 cm. We say that second resonance is obtained at 24 cm. What I don't understand is that when the length of air column is changed, doesn't its fundamental frequency of vibration change?

 

[Andrew Mason]

Sir,
I know that a tuning fork will vibrate only with a single frequency and resonance takes place when the frequency of the tuning fork becomes equal to the fundamental frequency of vibration of the air column. But in a resonance column we speak about first resonance say for 48cm length of air column. Suppose some water is poured into the resonance tube until resonance is obtained at another length say 24 cm. We say that second resonance is obtained at 24 cm. What I don't understand is that when the length of air column is changed, doesn't its fundamental frequency of vibration change?

A closed column, for example, resonates when the applied sound has a wavelength that is $\lambda = 4L, \lambda = 4L/3, \lambda = 4L/5 ...etc$ ie. when there is an anti-node at the open end. An open column has an anti-node at both ends.

AM

 

[Amith2006]

Sir,
You have said in your last reply that an air column of length L resonates with an applied sound when it has wavelengths of 4L,4L/3,4L/5... My question is that can a source of vibration of single frequency(say a tuning fork) produce vibration of different wavelengths? If so, how do you change the wavelength of source without changing affecting its frequency?
If that is the case, I think the velocity of the vibration changes with wavelength of vibration. Then only the frequency will remain the same. What do you say Sir?

 

[Hootenanny]

Sir,
You have said in your last reply that an air column of length L resonates with an applied sound when it has wavelengths of 4L,4L/3,4L/5... My question is that can a source of vibration of single frequency(say a tuning fork) produce vibration of different wavelengths? If so, how do you change the wavelength of source without changing affecting its frequency?
If that is the case, I think the velocity of the vibration changes with wavelength of vibration. Then only the frequency will remain the same. What do you say Sir?

The frequency of a wave is determined by the source, thus once generated the frequency of a wave never changes. The wavelength however, can be changed by altering the velocity as you say. However, the tuning fork will still produce soundwaves at its natural frequency, this said, you could increase the wavelength of the wave by making it travel through a less dense medium (sound travels slower the less dense the medium). However, it must be emphisised that the frequency of the source will not change without physically altering the source.

Hope this helps

~H

 

[arunbg]

Just to add to what Hootenenny said, the frequency of the resonance column can be altered by physical means, which in this case is varying the length of the air column.
Now a resonance column can resonate at different frequencies ( not just the fundamental frequency) known as modes of vibration,whose values in this case essentially depends upon the length of the column as AM pointed out.
Suppose at some length, the column in its first mode of vibration, resonates with the tuning fork , then for some other length it will resonate in its second mode and so on.
Now can you answer your question ?

 

[Amith2006]

Now I have understood Sir. Thanks to all of you.

 

[Andrew Mason]

Sir,
You have said in your last reply that an air column of length L resonates with an applied sound when it has wavelengths of 4L,4L/3,4L/5... My question is that can a source of vibration of single frequency(say a tuning fork) produce vibration of different wavelengths? If so, how do you change the wavelength of source without changing affecting its frequency?
If that is the case, I think the velocity of the vibration changes with wavelength of vibration. Then only the frequency will remain the same. What do you say Sir?

You have to look at the physics of a vibrating air column. A column closed at one end will resonate with any sound that can produce a node at one end and an antinode at the other: ie if it is 1/4 of the wavelength, 3/4, 5/4, 7/4 etc.

So if you start with a column that resonates because it is 7/4 of the wavelength of the source, it will resonate again at 5/4, 3/4 and 1/4 as you shorten the column. The frequency does not change, of course.

AM