Question

Vishanth took a rope of linear mass density of $0.04kg{m}^{-1}$ and a length of $3m$. He tied the rope tightly between the two walls and disturbed it to vibrate. He noticed that transverse wave is progressing in rope at a speed $xm{s}^{-1}$. If tension in the string is $1N,$ then $x=\_\_\_\_\_\_\_\_\_.$

• A. $5cm{s}^{-1}$
• B. $10m{s}^{-1}$
• C. $5m{s}^{-1}$
• D. $10cm{s}^{-1}$

Answer 1

The correct option is C

$5m{s}^{-1}$

Correct option is C: $5m{s}^{-1}$

Explanation:

Step 1: Given:

Linear mass density of string $\left(\mu \right)=0.04kg{m}^{-1}$

Tension on the string $\left(T\right)=1N$

Speed of wave $\left(v\right)=xm{s}^{-1}$

Find: Velocity $\left(v\right)=?$

Step 2: Finding velocity:

We know that, Velocity (v) velocity of wave in rope is given by,

$$\begin{gathered} v=\sqrt{\frac{T}{\mu }} \\ x=\sqrt{\frac{1N}{0.04kg{m}^{-1}}} \\ x=5m{s}^{-1} \end{gathered}$$

Hence, velocity x= 5 m/s