I have a loudspeaker that is facing into a long cylindrical piece of PVC pipe of length $L$. The loudspeaker is sealed in so that no air can escape around the edges. The pipe is open at the other end.

The system is modeled as an open pipe, because there are displacement antinodes at both the loudspeaker end and the open end (see Loudspeaker attached to cylinder - closed or open?).

The loudspeaker has a sensitivity of $S$ decibels at 1W/1m, and it is being fed an electrical sine wave of power $P$ at the fundamental resonant frequency $f_0 = \frac{c}{2L}$ where $c$ is the speed of sound.

A standing wave is established which causes the sound coming out of the open end of the pipe to be louder than it would be if there were no pipe at all.

I would like to know exactly how much louder. Specifically, I'm looking for a formula to calculate the SPL in decibels of sound coming out of the resonant tube, in terms of $S$, $P$, $f_0$, $L$ or any other relevant variables.

Any pointers would be greatly appreciated!


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