What is the function of the air cavity inside drums?

[Aethermimicus]

TL;DR Summary

I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.'
I'm struggling to understand the function of the air cavity in drums and I don't know how to calculate the resonance frequencies. (suppose there is only one membrane stretched over a cylindrical cavity).

I'm trying to understand the function of the air cavity inside drums.

I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.'

Then what are the resonance frequencies?

Is it the same as a Helmholtz resonator?
So when the drum membrane is vibrating, it squeezes the air inside the cavity. The air cavity acts like a spring.
But there are different modes of vibration for the drum membrane. Usually when some parts of the membrane are going up other parts are going down, then the air inside the drum is not being squeezed.

I'm struggling to understand the function of the air cavity in drums and I don't know how to calculate the resonance frequencies. Can someone help? (suppose there is only one membrane stretched over a cylindrical cavity).

 

[Baluncore]

Welcome to PF.

I'm trying to understand the function of the air cavity inside drums.

It is a very wide field, and the theory is not simple.
https://www.soundonsound.com/techniques/physics-percussion
https://www.idrumtune.com/drumhead-vibration-and-the-science-of-sound/

 

[sophiecentaur]

Welcome to PF.

It is a very wide field, and the theory is not simple.
https://www.soundonsound.com/techniques/physics-percussion
https://www.idrumtune.com/drumhead-vibration-and-the-science-of-sound/

I have to say that I was disappointed to read in the first reference
"how the tones of most real instruments can be reduced to patterns of harmonics, which can be generated using sine, saw, square or pulse waveforms".
In fact the sounds from all but the purest of instruments consist of overtones which often have spectral components which very far from harmonics. The frequencies depend on Modes of Oscillation of air, strings, diaphragms, reeds etc. For a drum skin, the modes are often described by Bessel functions. That article goes into a lot of detail about these modes and then shows how you actually can't synthesise musical instrument sounds using mixtures of harmonics - so why start off with the wrong premise?

 

[Aethermimicus]

Thanks! I've also found an article.
Christian, R.S., Davis, R.E., Tubis, A., Anderson, C.A., Mills, R.I., and Rossing, T.D.
(1984). Effects of air loading on timpani membrane vibrations. J. Acoust. Soc. Am.
76, 1336-1345.

 

[Vanadium 50]

Is this question "why aren't drums hundreds of pounds of solid plastic that don't sound like drums when you play them"?

 

[sophiecentaur]

Is this question "why aren't drums hundreds of pounds of solid plastic that don't sound like drums when you play them"?

I guess it's something like that.
One important reason for using a cavity would be to improve the coupling of the energy out as sound (impedance matching - that's a requirement for most instruments, to make them as loud as possible, as with the baffle on a loudspeaker).

One simple (dangerous) answer could be that the cavity could be acting like a low pass (?) filter, selectively coupling areas of the diaphragm together as the air sloshes from side to side so that areas going down are pushing corresponding areas up. Larger area modes would interact more than smaller area modes and that could account for the low pass filtering. And it's all very broad band because of the 3D cavity.
Conga drums are about 1m tall with a very low resonance -
It's a bit like a closed pipe and the simple resonance is at 4λ
f = c/λ = 330/4 which would be tuned to around 80Hz
That's the sort of frequency we hear from a conga so my cunning theory could be along the right lines.
Tympani have curved bottoms and are struck half way out to the edge which would encourage longer paths from side to side with no reflection; longer path than flat bottoms and hence lower frequencies.
Many simple drums have open bottoms and there will not be as much coupling or sound level. Many drums have diaphragms both sides (bass and snare) and I imagine the two diaphragms will have common modes.

 

[Vanadium 50]

There certainly is a mathematical analysis of the sound of drums (see e.g. Rossing) which will involve Bessel functions, but as stated it's hard to pin down what would satisfy the OP. Certainly the inventor of the drum, who I believe was the late Thag Simmons, didn't solve a bunch of Bessel functions to get the sound he wanted.

 

[tech99]

Summary: I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.'
I'm struggling to understand the function of the air cavity in drums and I don't know how to calculate the resonance frequencies. (suppose there is only one membrane stretched over a cylindrical cavity).

I'm trying to understand the function of the air cavity inside drums.

I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.'

Then what are the resonance frequencies?

Is it the same as a Helmholtz resonator?
So when the drum membrane is vibrating, it squeezes the air inside the cavity. The air cavity acts like a spring.
But there are different modes of vibration for the drum membrane. Usually when some parts of the membrane are going up other parts are going down, then the air inside the drum is not being squeezed.

I'm struggling to understand the function of the air cavity in drums and I don't know how to calculate the resonance frequencies. Can someone help? (suppose there is only one membrane stretched over a cylindrical cavity).

The drum is a pipe with a membrane over one end. The length of the pipe is much too short to resonate at low sound frequencies. It looks to me as if the drum is the same as a sealed speaker enclosure - the infinite baffle. In this case, sound from the rear of the diaphragm is prevented from radiating. The sound from the rear is antiphase from that from the front, so must be suppressed in order to obtain good low frequency action. The air behind the diaphragm acts as a spring and raises the fundamental resonance of the diaphragm to some extent. The fundamental frequency is determined by the mass of the diaphragm and the stiffness of its mounting, caused by the tension of the membrane and the volume of the backing enclosure. Higher resonances will occur due to overtone action on the membrane, in the manner of Chladni's Figures, which you might have seen in school science.
I suggest looking up the infinite baffle as a way of calculating the fundamental frequency of the drum.

 

[sophiecentaur]

The length of the pipe is much too short to resonate at low sound frequencies.

It's only for a drum of the shape like a conga that you have anything approaching a pipe but that closed tube will have a resonant mode at below 100Hz. A drum with two skins will involve both skins interacting as much as the skin / cavity.

A loudspeaker is a bit different, I think because, ideally, the cone is totally rigid and acts like an piston. The cavity in that case is more of a matching element, I think.

 

[tech99]

Yes I had not considered that there are two skins, so it looks as if the air is just a mass added to the membrane masses. For a modern speaker it is usually a sealed box, an infinite baffle, which contains friction material to absorb the sound. The box (undesirably) raises the speaker resonance and the overall device is very inefficient.

 

[sophiecentaur]

For a modern speaker it is usually a sealed box, an infinite baffle

Speaker design has many constraints and it's always a compromise. To extend bass range, a port is often used (Helmholz idea). A woofer is built all around that. Now you've brought it up, I'm surprised that bass drums don't use a ported cavity - although there's a lot of power available from the 'driver' so maybe it's just cheaper without.

 

[Andy Resnick]

Speaker design has many constraints and it's always a compromise. To extend bass range, a port is often used (Helmholz idea). A woofer is built all around that. Now you've brought it up, I'm surprised that bass drums don't use a ported cavity - although there's a lot of power available from the 'driver' so maybe it's just cheaper without.

Are you referring to these things?
https://www.musiciansfriend.com/acc...lVz3gL-ca58IhUGNF2wqYism8zKN0aZoaAvF9EALw_wcB

Or this?
https://www.musicradar.com/reviews/drums/drumport-drum-insert-525998

I have also seen a second (smaller) drum mounted over the front port of the kick, but can't easily find an image...

Edit- here it is, on Questlove's kit:

https://music.stackexchange.com/questions/62263/what-are-the-attachments-used-for-on-this-bass-drum

 

[sophiecentaur]

Are you referring to these things?

Exactly!