Question

A uniform string of length `L` and mass `M` is fixed at both end while it is subject to a tension `T`. It can vibrate at frequencies `v` given bby the formula (where, `n=1,2,3,………..)`
A. `v=(n)/(2)sqrt((T)/(ML))`
B. `v=(n)/(2L)sqrt((T)/(M))`
C. `v=(1)/(2n)sqrt((T)/(ML))`
D. `v=(n)/(2)sqrt((TL)/(M))`

Answer 1

Correct Answer - A
Mass per unit length of string, `m=M//L`
If the string vibrates in `n` segments and wavelength of wave is `lambda`, then
`L=(nlambda)/(2)`or `lambda=(2L)/(n)`
Velocity of transverse wave in string is
`upsilon=sqrt((T)/(m))=sqrt((T)/(M//L))=sqrt((TL)/(M))`
`:.` Frequency of oscillations is
`v=(upsilon)/(lambda)=sqrt((TL)/(M))xx(n)/(2L)=(n)/(2)sqrt((T)/(ML))`