Question

A long string having a cross-sectional area $0.8{\text{mm}}^2$ and density $12.5{\text{g/cm}}^3$, is subjected to a tension of $64\text{N}$ along the $x-$ axis . One end of this string is attached to a vibrator, which is vibrating in a transverse direction. Find the speed of the wave travelling on the string.

• A. $40\text{m/s}$
• B. $80\text{m/s}$
• C. $20\text{m/s}$
• D. $10\text{m/s}$

Answer 1

The correct option is B $80\text{m/s}$

Linear mass density$\left(\mu \right)$ is defined as mass per unit length of string.
$\mu =\frac{m}{l}$
Mass of the string will be,
$m=\rho \times V=\rho \times A\times l$

The linear mass density is,
$\Rightarrow \mu =\frac{\rho \times A\times l}{l}=\rho A$
$\mu =(12.5\times {10}^3{\text{kg/m}}^3)\times (0.80\times {10}^{-6}{\text{m}}^2)$
$\mu =0.01\text{kg/m}$.

The wave speed is,
$v=\sqrt{\frac{T}{\mu }}$
$\Rightarrow v=\sqrt{\frac{64\text{N}}{0.01\text{kg/m}}}=80\text{m/s}$.