How does the density of air affect the note you hear?

[rafk_1]

TL;DR Summary

How does pressurized air in a bottle change the sound of the note being played (more air = higher note) but what is the explanation behind why this works?

I'm making an instrument for a high school physics project and I was wondering how the density of air changes the perceived note and the explanation behind it. I've managed a few possible theories but none that I was fully confident in. I'll reference a video which inspired my idea, adding more pressurized air to the bottle changes the pitch but I'm not exactly sure how this could work, does anyone have any answers? Thanks for the help.
Plastic Bottle Marimba

 

[Baluncore]

Welcome to PF.
You are making a drum. The skin of the bottle is the membrane. When the bottle is struck it deforms, then it springs back to the original shape at a rate determined by the tension in the skin. The tension in the skin is determined by the internal air pressure. So the frequency of the note rises as the air pressure is increased.
It is not the density of the air, but the pressure that makes the difference.
https://en.wikipedia.org/wiki/Drum

 

[Vanadium 50]

Your ear measured frequency. It hears the same frequency as the source. The frequency of the source may or may not depend on the properties of air. A flue or organ pipe is different from an electronic loudspeaker.

 

[Hornbein]

I know that wind instruments play higher pitch in less dense air. This can be a problem for recording studios at high altitudes.

 

[nasu]

The instrument described in the OP is not a wind instrument. It is a percussion instrument where the air pressure is used to adjust the tension in the membrane.

 

[jbriggs444]

I know that wind instruments play higher pitch in less dense air. This can be a problem for recording studios at high altitudes.

To first order, pressure does not affect sound velocity and, hence, the resonant frequency for cavities of a given length. The reduction in density due to pressure cancels with the corresponding reduction in bulk modulus for an ideal gas. Are there some second order factors at play here?

You get a higher tone in a flute in a helium-oxygen atmosphere compared to a nitrogen-oxygen atmosphere. You do not get a higher tone for a 1/2 bar atmosphere compared to a 1 bar atmosphere.

To be clear, this would be relevant if we were discussing wind instruments and resonances due to the speed of sound in air. But we are actually discussing a percussion instrument. The resonances are due to the vibration of the instrument. Like the resonance of a violin string as it is being tightened.

 

[Hornbein]

To first order, pressure does not affect sound velocity and, hence, the resonant frequency for cavities of a given length. The reduction in density due to pressure cancels with the corresponding reduction in bulk modulus for an ideal gas. Are there some second order factors at play here?

You get a higher tone in a flute in a helium-oxygen atmosphere compared to a nitrogen-oxygen atmosphere. You do not get a higher tone for a 1/2 bar atmosphere compared to a 1 bar atmosphere.

To be clear, this would be relevant if we were discussing wind instruments and resonances due to the speed of sound in air. But we are actually discussing a percussion instrument. The resonances are due to the vibration of the instrument. Like the resonance of a violin string as it is being tightened.

I say this because when Earth Wind and Fire recorded in Colorado they complained that the high altitude made their wind instruments go sharp.

 

[Vanadium 50]

1. Just the wind instruments? The Earth and Fire instruments were OK?
2. Bands say a lot of things on stage - "Hello Muncie! It's great to be back! One of our favorite cities!"