A student uses an audio oscillator of adjustable frequency to measure the depth

Question

A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports hearing two successive resonances at 50.5 Hz and 59.5 Hz. How deep is the well?

A typical sound level for a buzzing mosquito is 37 dB, and that of a vacuum cleaner is approximately 67 dB. Approximately how many buzzing mosquitoes will produce a sound intensity equal to that of a vacuum cleaner?

How far, and in what direction, should a cellist move her finger to adjust a string's tone from an out-of-tune 446 Hz to an in-tune 440 Hz? The string is 68.0 cm long, and the finger is 21.9 cm from the nut for the 446-Hz tone.

Explanation / Answer

First we need the vibrating length

68 - 21.9 = 46.1 cm

v = f(wavelength) and v will remain constant, so

f(wavelength) = f(wavelength)

(446)(2)(.461) = (440)(2)(x)

x = .4673 m

Since the string length is .68, then .68 - .4673 = .213 m

.219 - .213 = .00629 m which is .629 cm or 6.29 mm toward the nut

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