# A student uses an audio oscillator of adjustable frequency to measure the depth of a water well....

## Question:

A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. The student reports hearing two successive resonances at 52.15 Hz and 60.50 Hz. (Assume that the speed of sound in air is 343 m/s.)

(a) How deep is the well?

(b) How many antinodes are in the standing wave at 52.15 Hz?

## Resonance in Closed Air Columns

When mechanically driven, cylindrical air columns are able to support standing sound waves. The frequency {eq}f {/eq} of the supported wave depends on the length {eq}L {/eq} of the tube, on the speed of sound {eq}c {/eq} in the surrounding gas and whether the tube is closed or open on one end. The other end has to be open.

The frequency supported by the closed tube is {eq}f = c / 4 L {/eq} and odd harmonics thereof. The frequency supported by the open tube is {eq}f = c / 2 L {/eq} and all harmonics thereof. Harmonics are integer multiples of the fundamental frequency {eq}f {/eq}.

Since we are given the she speed of sound in air (c = 343 m/s), we assume that the well is empty and that the reported resonances are generated by...

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