A string in a musical instrument is `50 cm` long and its fundamental frequency is `800 Hz`. If the frequency of `1000 Hz` is to be produced then required length of spring is

Options

A. `62.5 cm`
B. `50 cm`
C. `40 cm`
D. `37.5 cm`

Answer

C

Explanation

The frequency produced in a string of length `l`, mass per unit length `m`, and tension `T` is
`n=(1)/(2l)sqrt((T)/(m))`
Given `l_1=50cm,n_1=800Hz`
and `n_2=1000Hz`
`n_1l_1=n_2l_2`
`implies800xx50=1000xxl_2`
`impliesl_2=40cm`