Calculating Resonant Frequency of Water in a Cylindrical Pipe

[petmar]

i have a cylindrical pipe with a fixed internal diameter and a variable length. how would i calculate the resonant frequency of water within it, given that the speed of sound in water is approx. 1398 m/sec?

 

[zoobyshoe]

Fascinating question. Perhaps without realizing it you have posed a trick question. I thought about it a long time.

Water, like air, is a medium of sound.

Any object has a resonant frequency which can be found. If you find it, and cause the object to vibrate at that frequency, it will be very easy to keep the object vibrating at that frequency because its resonant frequency is the one at which it most wants to vibrate.

All that is immaterial. You are asking what the resonant frequency of the medium that carries the frequency might be. If we define sound as waves in air, or waves in water, is it really possible to ask what the resonant frequency of air or water is? This makes me wonder, too, if we should ask if there is a frequency at which the Elecro-Magnetic spectrum might prefer to oscillate? Let's say your pipe is made of steel. Can we ask what the resonant frequency of steel is?

Perhaps the speed of sound itself constitutes the resonant frequency of air, and likewise for water. I'm not sure.

It could be that you want to know what the resonant frequency of the length of pipe would be under water, and if that would be different than in air. It's hard to say. (Its hard to say what information would best answer your needs, I mean.)

 

[petmar]

well, what i actually am looking for is the correlation between internal area, which would correlate with intensity, and length, which would correlate with λ, wavelength. from λ=v/f, i can then tell the rest of the story. that's all.

would it be easier if i were to say that the diameter and length are constant, while the frequency can be varied?

 

[zoobyshoe]

I still don't understand if you want the resonant frequency of the pipe, or the resonant frequency of the water it can contain.

 

[petmar]

the...

pipe!

 

[zoobyshoe]

Excellent choice!

I have no idea how to do it but I believe it can be done. My book of physics formulas had nothing for this situation, but I will bet Integral, at least, will know the way to go about it.

I will be intrigued, too, to see if anyone has anything interesting to say about the notion that water or air might, themselves, have a resonant frequency. It is a question I never thought to ask.

So, be patient, and someone should come along with some insight.

-Zooby

 

[russ_watters]

This is a first semester fluids problem. What you really want is not a resonant frequency of a pipe or a resonant frequency of some water, but the resonant frequency of a pipe with water in it.

IIRC, its simply a matter of dividing the speed of sound in water by twice the length of the pipe. I don't have time to look it up right now though.

 

[Integral]

I do not think area has much to do with it. Length on the other hand is the key. The tube length, or water depth, must be a multible of the wavelength of sound in your medium. Frequency = ν s= speed of sound in water, l= the length of your tube.


ν_n=ns/2l

I find for water a 25c s=~1500m/s

given a 1 m tube length (assuming the tube is full)

ν₁= 750Hz