an instrument consists in a series of long metal cylinders, each of length x and

Question

an instrument consists in a series of long metal cylinders, each of length x and diameter x/10. the cylinders are closed at one end and open at the other. A string is stretched across the open end. The string has mass per unit length and tension T. the string is put under enough tension so that the dundamental frequency of the waves in the vibrating string equals the n=3 mode of the sound waves in the cylinder. derive a formula for the tension in the string in terms of the other parameters of the instrument and the speed of sound in air, v.

Explanation / Answer

Let the Tension be T.
For standing waves on string,

f = V'/2L ; L = x/10.

f = sqrt (T/)*5 / x

Underr the same case, The frequency of pipe is 3f,

f = 3*V/4L ; L = x

f = 3V/4x

Equating, sqrt(T/)*5 = 3V/4

T/ = 9V2/400

T = 9V2/400.

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