Question

A string of mass ‘M’ is under a tension ‘T’. The length of the string is ‘L’. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is ______.

पर्याय

• `sqrt(T/(ML))`

• `sqrt((LT)/M)`

• `sqrt(M/(LT))`

• `sqrt((ML)/T)`

Answer 1

A string of mass ‘M’ is under a tension ‘T’. The length of the string is ‘L’. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is `bbunderline(sqrt((ML)/T))`.

Explanation:

The speed of a transverse wave on a string depends on the tension (T) and the linear mass density (μ).

v = `sqrt(T/mu)`

This is the mass per unit length of the string.

`mu = M/L`

Substituting μ:

v = `sqrt(T/(M//L))`

= `sqrt((TL)/M)`

Time is distance (L) divided by velocity (v),

t = `L/v`

= `L/(sqrt((TL)/M))`

= `sqrt((L^2 * M)/(TL))`

= `sqrt((ML)/T)`