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The sound pressure level of an organ pipe is a function of the gas flow rate delivered to the pipe. Source

Would the sound level of an organ pipe driven by helium be lower than that of a pipe driven by air at the same blowing pressure (same volume flow rate) due to the lesser mass flow rate of the helium (helium being of lesser density than air)?

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In Blake 1986 'Mechanics of Flow-Induced Sound and Vibration V1: General Concepts', pg. 148 the author provides a helpful equation for the pressure radiated by organ pipes when the cavity is small compared to a wavelength, i.e., $\lambda_0 \gg$ cavity dimensions. (Note this is the usual approximation for organ pipes, which are considered 'acoustically small'.)


$$\frac{\lvert p_{\ radiated}\rvert}{\lvert p_{\ cavity}\rvert} = \frac{\omega A_0}{c_0 \ r}$$

where $\omega$ is the resonant frequency of the pipe (cavity),

$A_0$ is the area of the pipe's opening,

$r$ is the radius of the pipe, and

$c_0$ is the speed of sound in the pipe.


Given the same pipe and flow rate, $A_0$ and $r$ drop out of the equation.

The speed of sound in helium is obviously different than air, and so $c_0$ decreases. For a pipe of length $L$, the resonant frequency $\omega = \frac{c_0}{2L}$, so the decrease in sound speed found in the denominator is canceled by a matching decrease in the numerator. We are left with a factor of $2L$ which also will not change.

This suggests that the pressure radiated by the organ pipe should not change with the density of the gas.

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