A tuning fork with a frequency of 256 s-1 is held above a cylinder of length h.

Question

A tuning fork with a frequency of 256 s-1 is held above a cylinder of length h. The cylinder is gradually filled with water (i.e. x in the diagram below gradually increases.) For certain values of x, a standing wave is created in the air column above the water, amplifying the sound created by the tuning fork. (This occurs when the length of the air column above the water is such that the air column has a standing wave mode with the frequency of the tuning fork.) Find the values of x for which this occurs. Take h = 2.00m. Take the speed of sound to be 345 m/s.

Explanation / Answer

The length of the tube is H = 2 m

The speed of the sound is v = 345 m/s

As the cylender 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

256 = n 345/4L

For n= 1

256 = 345/4L

L = 0.337 m

x1 = 2 m - 0.337 m = 1.663 m

For n= 3

256 = 3*345/4L

L = 1.011 m

x2 = 2 m - 1.011 m = 0.989 m

For n= 5

256 = 5*345/4L

L = 1.685 m

x2 = 2 m - 1.685 m = 0.315 m

For the water coloumn heights, 0.315 m, 0.989 m and 1.663 m resonance will occur

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