Question

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

Options

• 300 Hz

• 500 Hz

• 100 Hz

• 400 Hz

Answer 1

Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by 1%, 3 beats are produced in 2 s. The initial frequency of vibration of each wire is 300 Hz.

Explanation:

The frequency of vibration,

`n = 1/(2l)sqrt(T/m)`

Given, `n^' = n + 3/2`

and `T^' = T + 1%  "of"  T = T + T/100 = (101T)/100`

`n^' = 1/(2l)sqrt(T^'/m)`

∴ `n + 3/5 = 1/(2l)sqrt((101T)/100)`

⇒ `n + 3/2 = 1.005 xx 1/(2l)sqrt(T/m)` .........(ii)

From Eqs. (i) and (ii), we get

`n + 3/2 = 1.005 + n`

⇒ n = 300 Hz