A person hums in a well and finds strong resonance at frequencies 60Hz, 100Hz and 140Hz. What is the fundamental frequency of the well? Explain? How deep is the well? (velocity of sound=344m/s).
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(fundamental frequency n = 20 Hz, depth of the well = 4.3)
The well can be considered as an organ pipe closed at one end and open at the other. At the fundamental mode, λ/4 = λ (depth of the well in this case). The given frequencies happen to be 3rd, 5th & 7th harmonics of the fundamental frequency n = 20 Hz. Now use v = nλ so as to obtain depth of the well = 4.3 m.
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