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}.

Answer and Explanation:

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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Interference Patterns of Sound Waves

from MTEL Physics (11): Practice & Study Guide

Chapter 16 / Lesson 5
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