Forming a standing sound wave in a wind instrument

[davidbenari]

So I've had this question bugging me ever since I saw sound at physics class:

How is it possible to match the resonance frequency of a column of air in an organ pipe and form a standing sound wave by simply blowing air into the column?

The main reason I see this problematic is because I can't figure out how a continuous stream of air (what I blew in) would make it possible for there to be parts of the air column which are not moving at all (namely, the nodes in the standing wave).

In a simple way, how does this work? (Blowing air and creating a standing wave pattern)

Thanks.

 

[Ayesha_Sadiq]

I am not exactly sure, but when you blow air into an organ pipe, the stream of air splits into two. One going through the pipe, the other going around the outside of the pipe. A wavering sort of vibration is set up. And when the frequencies of the vibrations are right, stationary waves are produced. Have a look at this : http://www.tutorvista.com/content/physics/physics-iii/waves/vibrations-in-pipes.php
Most of the air you blew in gets out I guess.
And you might also like this : http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
The Animations are great.

 

[sophiecentaur]

How is it possible to match the resonance frequency of a column of air in an organ pipe and form a standing sound wave by simply blowing air into the column?


In a simple way, how does this work? (Blowing air and creating a standing wave pattern)

Thanks.

The full details involve some difficult Maths and most treatments just concentrate on the frequency selection that you get with a standing wave but there is more to it than that.

It is all a matter of both 'Matching' and frequency selection. Sometimes a reed is used and sometimes a slot (as with a recorder) or a string. As air passes over these structures they can cause vibrations over a very wide band of frequencies (random turbulence). Just put your lips together and blow and you will hear a simple wideband hiss.

The concept of Impedance Matching applies to waves passing from one medium or structure to another. If a wave in a high impedance structure (say a tuning fork) hits a low impedance medium (air) then very little sound gets transferred (hardly any air gets disturbed. If you match into the air, using a table top, lots of air is moved and much more sound energy gets out. The impedance of the air at the organ blower / mouthpiece is only matched to the pipe at frequencies relating to the fundamental and overtones of the pipe.

In order to produce a musical note, you need to have a resonance - air column. At the resonant frequency, the mechanical impedance of the resonant structure (air column) is the same as the impedance of the turbulent air at that frequency. Energy will pass from the turbulent air into the resonator - at one particular frequency. Energy at this frequency is, in effect, 'sucked out of' the turbulent area. If you try blowing a trumpet, you can actually feel when you make a note successfully that it becomes easier to blow than it is when making a general farting noise. This, again, is when you have matched energy into the air column. Energy at other frequencies doesn't build up and, more than that, is not accepted into the resonator.

When a bow rubs against a violin string, there is a similar process of a random scraping 'hiss' getting channeled into a resonant note on the string.

 

[AlephZero]

I think there are two parts to the OP's question:

1. Sound waves are perturbations of any underlying global motion. For example two people can talk to each other even if there is a strong wind blowing, and the velocity of the air is not zero anywhere. The "zero velocity at a node" means the perturbation is zero at that point, not the velocity of the air is zero.

2. If you just blow air into a pipe at one end, you won't produce a sound. Organ pipes work by blowing air across a hole in the side of the pipe, like blowing air across the top of a bottle. The details of exactly how this works are complicated, and the currently accepted explanation has only been around for about 40 years, which is nothing compared with the length of time people have been making musical instruments with pipes!

The diagram in http://www.tutorvista.com/content/ph...s-in-pipes.php is the right idea but the proportions are wrong, and I can't imagine why any real organ builder would make a pipe with that solid quarter-circle shape! For a better description of the physics see http://www.physics.unsw.edu.au/music/people/publications/Fletcheretal1983.pdf
http://www.physics.unsw.edu.au/music/people/publications/Fletcheretal1983.pdf

 

[olivermsun]

When a bow rubs against a violin string, there is a similar process of a random scraping 'hiss' getting channeled into a resonant note on the string.

Just a note that in this special case, there is no "random scraping" at all getting resonantly amplified!

 

[olivermsun]

2. If you just blow air into a pipe at one end, you won't produce a sound. Organ pipes work by blowing air across a hole in the side of the pipe, like blowing air across the top of a bottle.

Here is a nice explanation for the airflow in a recorder (a "longitudinal" flute), which is similar to the case of organs (and whistles, at the other end of the size scale!). Despite the perception that one is blowing air along the column, that isn't quite what's going on, and indeed what you are doing is blowing air across the top of the oscillating (resonant) air column.

 

[sophiecentaur]

Just a note that in this special case, there is no "random scraping" at all getting resonantly amplified!

Are you saying that the rosin / hair / stickiness is all part of a relaxation type oscillator? That sounds like a better explanation. Could that also apply to brass instruments, I suppose? (Both being non-linear effects).
What about the energy in the turbulence in the organ pipe whistle? Is there also some non linearity there that has the same effect? It would be much more efficient if it worked that way.
I must say, the resonance part of this topic is a lot easier to understand than the actual sound production bit.

 

[olivermsun]

Are you saying that the rosin / hair / stickiness is all part of a relaxation type oscillator? That sounds like a better explanation. Could that also apply to brass instruments, I suppose? (Both being non-linear effects).
What about the energy in the turbulence in the organ pipe whistle? Is there also some non linearity there that has the same effect? It would be much more efficient if it worked that way.

The rosin actually goes through repeated phase changes so that it glues/unglues the bow hair to the string, producing a characteristic sawtooth wave. This is why you get the surprising result that the bowed instrument gets louder when you use more bow speed, not more pressure!

The turbulent flow for the organ pipe alternates its path past the labium (the wedge shaped part behind the "slot" in the tube) so in some important sense it is a similar feedback mechanism.

Reeds or the player's lips in a brass instrument could oscillate on their own, but I suppose the basic phenomenon is again the same — the reed or the lips are actually the generating "instrument," which is then coupled to a larger instrument!

 

[sophiecentaur]

So we have a true oscillator, in every case then? A power source and a non linearity, which is coupled to a resonator. Just like a Gunn diode microwave source! That seems fair enough to me. The common view that it's simple filtering involved (what I was implying at the top) is far too superficial for a satisfactory explanation.

 

[AlephZero]

So we have a true oscillator, in every case then? A power source and a non linearity, which is coupled to a resonator.

That's pretty much the current mainstream theory. If you want more detail, browse around
http://www.physics.unsw.edu.au/music/people/fletcherpublications.html