Harmonics in a closed pipe

alan4cult

Right, this is really bugging me.

If you strike a tuning fork of frequency, lets say 400Hz, and hold it over a closed pipe you will set up a wave of frequency 400Hz in the pipe right? So when you raise the pipe up and down you will get regions of strong resonance at the antinodes (1/4 wavelength, 3/4 wavelength, 5/4 wavelength...). Will all of these resonant sounds be at the same frequency? I think they are because the frequency is constant and the speed of sound in air is constant?

I'm doing LC Physics and I absolutely hate this chapter but I want to understand it more. My book says that you can set up overtones in a closed pipe and get different harmonics but I just don't get this. If a tuning fork vibrates at the fundamental frequency why would there be overtones? and also my book says that the next antinode will be the second harmonic. How can you have a second harmonic if you only have the fundamental frequency of the tuning fork?

Sorry it's so long but I hope you get my drift!

Michael Collins

If you strike a tuning fork of frequency, lets say 400Hz, and hold it over a closed pipe you will set up a wave of frequency 400Hz in the pipe right?

Assuming this pipe is open at one end, there are certain conditions that must be met before the wave will be set up. These conditions are called "boundary conditions" and they arise because the pipe is closed at one end. The conditons are: the vibration at the closed end must be zero (i.e. a node) and at the open end it must be a maximum (i.e. an antinode). So if all these are met you will indeed hear a loudish note at the frequency of the tuning fork.

So if you draw the waves in the pipe, the only way this can occur is if the pipe is of length either: 1/4 quarter of the tuning fork wavelength or 3/4 the wavelength or 5/4 etc.

So when you raise the pipe up and down you will get regions of strong resonance at the antinodes (1/4 wavelength, 3/4 wavelength, 5/4 wavelength...).

I'm assuming here the pipe is changing its effective length (if I remember my LC Physics correctly, by having the pipe partially dipped into water?).

In which case yes, first the pipe reaches 1/4 wavelength and you hear it resonating, then 3/4 and you hear it again etc, all at the same freqeuncy of the tuning fork.

My book says that you can set up overtones in a closed pipe and get different harmonics but I just don't get this. If a tuning fork vibrates at the fundamental frequency why would there be overtones?

OK so I think this is where you may be getting confused. Your book talks about what frequencies are allowed in a specific pipe. Obviously a tuning fork will only create one frequency in the pipe*, provided the conditions i mentioned above are met. Now if you don't change the length of the pipe, the next frequency that will be allowed is 3 times that frequency. So the only frequencies that are allowed in a pipe that is closed at one end are the fundamental frequency (f) and all the odd harmonics (3f, 5f, 7f etc). These won't be present unless you have a tuning for that frequncy though!


*Strickly speaking there will be a tiny amount of other frequencies present too as the vibration is not strictly sinusoidal i.e. not a perfect sinewave. But these would be fairly weak and hard to hear. This fact is well beyond LC though, so I wouldn't worry about it.

alan4cult

Thank you very much.
All is understood now.