A vertical cylinder of length L = 1.00 m can be filled with water to any level,

Question

A vertical cylinder of length L = 1.00 m can be filled with water to any level, so that an air column of length L ' 1.00 m exists in the part of the cylinder above the water. See the figure. The air column is open at the top, but closed at the bottom by the water. A tuning fork of frequency 686 Hz is set vibrating above the top of the cylinder. The speed of sound is 343 m/s. (a) Determine all of the lengths L' for which standing waves will resonate in this air column. (b) Sketch each of the waves resonating at these lengths, approximately to scale with one another

Explanation / Answer

The length of the tube is H = 1 m

The speed of the sound is v = 343 m/s

As the cylinder is closed at one end,The resonance occur at f = n. v/4L n = 1,3,5,.......

Where L is the length of the air coloumn given by L = H - x

The frequency of the tuning fork is f = 256 /s

686 2 = n * 344/4L

so

For n= 1, L = 343/(686 *4) = 0.125m

x1 = 1 - 0.125 = 0.875 m

For n= 3, L = 3* 0.125 = 0.375 m

so x2 = 1-0.375 = 0.625 m

For n= 5, L = 5* 0.125 = 0.625 m

x3 = 1-0.625 = 0.315 m

For the water coloumn heights, 0.315 m, 0.625 m, 0.125 m resonance will occur

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