Two ropes of same material of radius R and R/2 . What will be the ratio of wave speed in second rope to first?

Question

Two ropes of same material of radius R and \(\frac{R}{2}\) . What will be the ratio of wave speed in second rope to first? (They both are with same tension)

Answer 1

Answer is : 2

\(\mu = \frac{\pi R^2l\rho}{l} = \pi R^2 \rho\)

So, \(v_2 =\sqrt{\frac{5\pi}{\pi \rho R^2}}\)

\(v_1 = \sqrt{\frac{\tau}{\pi R^2\rho}}\)

\(\therefore \frac{v_2}{v_1} =2\)