Question

A metallic wire of $1m$ length has a mass of $10\times {10}^{-3}kg$. If the tension of $100N$ is applied to a wire, what is the speed of the transverse wave?

• A. $100m/s$
• B. $10m/s$
• C. $200m/s$
• D. $0.1m/s$

Answer 1

The correct option is A

$100m/s$

Step 1: Given data

Length, $l$$=$$1m$

Mass, $m=10\times {10}^{-3}kg$

Tension, $T=100N$

Step 2: Find mass per unit length $\mu$:

$\mu =\frac{m}{l}$

$\Rightarrow \mu =\frac{10\times {10}^{-3}}{1}$

$\Rightarrow \mu =10\times {10}^{-3}kg{m}^{-1}$

Step 3: Find the speed of the transverse wave

In a transverse wave, the particle displacement is perpendicular to the direction of wave propagation.

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

$$\begin{gathered} \Rightarrow v=\sqrt{\frac{100}{10\times {10}^{-3}}} \\ \Rightarrow v=100m/s \end{gathered}$$

Hence, option (A) is correct.