Two instruments having stretched strings are being played in unison . When the tension in one of the instruments is increases by ` 1% , 3` beats are produced in ` 2 s`. The initial frequency of vibration of each wire is

Options

A. 300 Hz
B. 500 Hz
C. 1000 Hz
D. 400 Hz

Answer

A

Explanation

The frequency of vibration
` n = ( 1 )/( 2l ) sqrt ((T) /(m)) " " `…(i)
Given `n' = n + ( 3 ) /( 2 ) `
and `T' = T + ( T) / ( 1 00) = ( 101T)/( 100 ) `
` therefore n + ( 3 )/ ( 2) = ( 1 )/( 2l ) sqrt (( 101T) /( 100 m) ) `
` rArr n + ( 3 ) / ( 2) = 1.005 xx ( 1)/( 2l ) sqrt (( T) /(m)) " " `...(ii)
From Eqs (i) and (ii) , we get
`n + ( 3 ) /( 2 ) = 1.005 xx n rArr n = 300 Hz `