The shaft for a well consists of a long tube that is open at the top and closed

Question

The shaft for a well consists of a long tube that is open at the top and closed at the bottom. To determine the depth of the well you place a speaker at the top of the shaft and find that you can create a resonant standing wave in the shaft (not the fundamental) that has a frequency of 136 hertz. As you slowly increase the frequency, you find that the next resonant standing wave that you can create has a frequency of 152 hertz. The speed of sound is 338 m/s Based on this information, what is the fundamental frequency for this shaft? b) how deep is the well? a)

Explanation / Answer

a) the difference between two consecutive resonant frequency is = 152-136 Hz=16 Hz.

If fundamental frequency is f then 2*f=16 which gives f=8 Hz.

b) The fundamental wavelength is =338/8=42.25m

Thus the depth of the well is= 42.25/4 =10.56m

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