The tension in a piano wire is `10 N`. The tension ina piano wire to produce a node of double frequency is

Options

A. `20 N`
B. `120 N`
C. `10 N`
D. `40 N`

Answer

D

Explanation

The frequency of note emitted by the wire,
`n=(1)/(2l)sqrt((T)/(m))`
`m=` mass `m` per unit length of wire and `T=` tension, and `l=` length of wire.
`(n_1)/(n_2)=sqrt((T_1)/(T_2))`
Given `T_1=10N,n_1=n` and `n_2=2n`
`implies(n)/(2n)=sqrt((10)/(T_2))impliesT_2=10xx4=40N`