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A wire of length 80 cm has a frequency o...

A wire of length 80 cm has a frequency of 256 Hz. Calculate the length of a similar wire under similar tension, which will have frequency of 1024 Hz.

Text Solution

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Given : `f_1 = 256 Hz, l_1 = 80 cm, f_2 = 1024 Hz`
The frequency of sound produced by a stretched wire
`f prop (1)/(l) or ` f l= constant
` therefore f_2 l_2 = f_1 l_1 = f_1 l_1 or l_2 = (f_1 l_1 )/(f_2 ) = ( 256 xx 80 )/( 1024 )= 20 cm `
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