Question

A $5.5metre$length of the string has a mass of $0.035kg$. if the tension in the string is $77N$, the speed of a wave on the string is

• A. $110m{s}^{-1}$
• B. $165m{s}^{-1}$
• C. $77m{s}^{-1}$
• D. $102m{s}^{-1}$

Answer 1

The correct option is A

$110m{s}^{-1}$

Step 1: Given data

Length of the string, $L=5.5m$

Mass of the string, $m=0.035kg$

Tension in the string, $T=77N$

Step 2: Find linear mass density, $\mathit{\mu }$

Linear mass density, $\mu =m/L$

$=\frac{0.035}{5.5}kg/m$

Step 3: Find the speed of a wave on the string, $\mathit{v}$

The speed of a wave on the string, $v=\sqrt{\frac{T}{\mu }}$

$$\begin{gathered} =\sqrt{\frac{(77x5.5)}{0.035}} \\ =110m/s \end{gathered}$$

Hence, option (A) is correct.