As a take-home lab exercise, a couple of physics students are measuring the dept

Question

As a take-home lab exercise, a couple of physics students are measuring the depth of a water well using sound resonance. They have a function generator, amplifier, and speaker through which they can play tones between 75.0 Hz to 150.0 Hz. They notice distinct resonances at 91.0 Hz, 117 Hz, and 143 Hz, but no other frequencies in the 75-150 Hz range cause resonance within the well. Note that a well is effectively a tube open on one end (the top) and closed at the other end (the bottom, by water usually.) If the speed of sound in air is 340.0 m/s, what is the depth of the well?

Explanation / Answer

an open ended tube

(2n+1)*f = 91 Hz

(2n+3)*f = 117 Hz

divide 1 and 2

(2n+1) / ( 2n+3) = 91/117

solving this n = 3

f = 13 Hz

wavelength = v/f = 340/13

and L = wave length / 4 = 6.538 m

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