Question

A uniform wire of length 20 m and weighing 5 kg hangs vertically. If g = 10 m $s^{-2}$, then the speed of transverse waves in the middle of the wire is:

• A. 10 m$s^{-1}$
• B. 10$\sqrt{2}$ m $s^{-1}$
• C. 4 m $s^{-1}$
• D. 2 m $s^{-1}$

Answer 1

Answer: (A)

10 m$s^{-1}$

Here $\mu =\frac{5}{20}kg/m=\frac{1}{4}kg/m$

Tension in the middle of wire,

$T=$ weight of half the wire $=\frac{5}{2}\times g=\frac{5}{2}\times 10N=25N$

As,$v=\sqrt{\frac{T}{\mu }}$

$\Rightarrow v=\sqrt{\frac{25}{1/4}}=10m/s$