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/100 = (101T)/100`
`therefore n+ 3/2=1/(2l)sqrt((101T)/(100m))=1.005xx1/(2l)sqrt(T/m)...(ii)`
From Eqs. (i) and (ii), we get
`n+3/2=1.005xxn rArr n = 300` Hz