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)?


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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