Airflow trough the pipe produces sound

[hemmul]

Good day, gentlemen!

A friend of mine asked me a question - he is making a project regarding the influence of the cavity shape on the spectrum of acoustic waves produced after "blowing" into this pipe. You know, many national instruments are based on a principle of the usual pipe.
Actually, the goal of the project is a creation of a software that will simulate any musical instrument...
Well, starting up with a simple model, let's consider a tube - open from both ends. we blow in one end, and the tube produces certain sound. He states (he measured/analysed the spectrum) that the produced frequencies depend linearly on the length of the tube. e.i. actually, the waves only of such wave lengthes appear, that have nodes/peaks on the endpoints of the pipe.

does it make any sense?
can you just give a brief explanation on the phenomenon?
i have my own ideas regarding this specific pipe case, but surely it's better to hear yours also ;)

Thanks in advance!

 

[chroot]

The sounds produced by musical instruments are universally due to standing waves inside the instrument.

Given a simple open-ended pipe, the ends of the pipe are always anti-nodes for displacement (places where the air moves most rapidly) and nodes for pressure (places where the pressure is constant).

The pitch of the notes produced by such an instrument indeed do depend on its length. Each possible pitch is one of many modes of vibration which might be setup inside the tube. The lowest possible such pitch is called the fundamental mode, and its frequency depends linearly on the length of the tube.

Here's a simple website on the topic: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

You should be able to find a wealth of additional information about standing waves in any basic college physics textbook, as the subject is quite well-understood.

- Warren

 

[The Bob]

Few websites:
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/waves/swf.html
http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html
http://www.phys.unsw.edu.au/~jw/strings.html

Chroot has said a fair amount. You get antinodes of sound at the open-ends and you also need to consider end-correction for accurate frequency calculations.

I resently did a project on standing waves and I have lots of calcuations and equations, which can be found on the net. If you can ask some more specific questions then more help might be available.

The Bob (2004 ©)

 

[hemmul]

Thanks chroot, thanks The Bob,
i have looked through the lins - basically i understand that the sound is due to the standing waves, and it is clear how the vibrating string works (the theory behind the wave equation is not that cumbersome ;))
So, talking more specifically, i "can't get" why

Given a simple open-ended pipe, the ends of the pipe are always anti-nodes for displacement (places where the air moves most rapidly) and nodes for pressure (places where the pressure is constant).

there is "air flow" through the pipe isn't it? according Bernoulli's law the average pressure inside is lower than atmospheric pressure (of course it oscillates due to the sound wave, that is why i used "average"). So the average density is also lower. That means, that velocity of sound is different in two media. That is we have to consider specific "boundary conditions" on the endpoints, that is it is a typical-normal-incidence-of-a-plane-wave-onto-a-boundary-of-two-media problem. isn't it? it is the explanation that i see, but it doesn't yet mean that the pressure is really constant at the ends... does it?