Question

What happen to the frequency of transverse vibration of a stretched string if its tension is halved and the area of cross section of the string is doubled?

Answer 1

Answer:

The fundamental frequency of the stretched string is:

$f=$ $\frac{1}{2} \sqrt{\frac{T}{L} }$ [ T = Tension and μ = mass per unit length]

Here,

 μ = $\frac{m}{L} = \frac{Vp}{L} = Ap$

$f= \frac{1}{2} \sqrt{\frac{T}{Ap} }$

If T is halved and A is doubled,

$f= \frac{1}{2} \sqrt{\frac{T'}{A'p} } = \sqrt{\frac{1}{2* 2* A* p} } = \frac{1}{2} (\frac{1}{2} \sqrt{\frac{T}{Ap} } = \frac{1}{2} f$

Thus, the frequency is reduced to half if its tension is halved and the area of cross-section of the string is doubled.