A vibrating tuning fork is held above column of air. Reservoir is raised and low

Question

A vibrating tuning fork is held above column of air. Reservoir is raised and lowered to change water level and length of column of air. Shortest length of air that produces resonance is .25. Next resonance is heard when air column is 0.80m long speed of sound in air is 343 m/s and spped of sound in water is 1490 m/s Wavelength of standing wave is 1 m frequency that produces this standing wave is 343 Hz wavelength of sound wave is 4.34 m

The water level is lwered again until a third resonance is heard. Calculate the length of air column that produces this third resonance

Explanation / Answer

The usual assumption is that the standing wave in the pipe has an antinode at the open end and a node at the water. Thus, the shortest air column corresponds to 1/4 wave, and the next column to 3/4 waves.

The wave equation is v = f ? where v is the velocity of sound in air, f the frequency, and ? the wavelength.

(a) 1/4 ? = .25 m so ? = 1.0 m
3/4 ? = .80 m so ? = 1.1 m

So the wavelength is just over one meter.
We'll just use 1 m for the rest of the problem.

(b) Using the wave equation, 343 m/s = f ( 1.0 m ) so f = about 343 Hz

(c) The next resonance occurs when the length of the air column is 5/4 ?

5/4 (1.0 m ) = about 1.2 m.

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