Question

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

• A. $10m/s^{-1}$
• B. $0.1m{s}^{-1}$
• C. $100m{s}^{-1}$
• D. $200m{s}^{-1}$

Answer 1

The correct option is C

$100m{s}^{-1}$

Step 1. Given data:

Length, $l=1m$

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

Tension,$T=100N$

Step 2. Find the linear mass density:

Linear mass density, $\mu =\frac{Mass}{Length}$

$$\begin{gathered} =\frac{10\times {10}^{-3}kg}{1m} \\ =10\times {10}^{-3}kg/m \end{gathered}$$

Step 3. Find the speed of transverse wave:

Speed of the transverse wave, $v=\sqrt{\frac{T}{\mu }}$

$$\begin{gathered} =\sqrt{\frac{100N}{10\times {10}^{-3}kg/m}} \\ =100m{s}^{-1} \end{gathered}$$

Hence, option (C) is correct.