Question

A string of density $7.5g/{cm}^{-3}$ and area of cross-section $0.2{mm}^2$ is stretched under a tension of 20N. When it is plucked at the mid point, the speed of the transverse waves on the wire is:

• A. 116 m/s
• B. 40 m/s
• C. 200 m/s
• D. 0 m/s

Answer 1

Answer: (A)

116 m/s

Density of string $\rho =7.5g/c{m}^3$
Cross-sectional area $A=0.2m{m}^2=0.002c{m}^2$
Thus mass per unit length of string $\mu =\rho A=\left(7.5\right)\left(0.002\right)=0.015g/cm$
$⟹\mu =0.015g/cm=0.0015kg/m$
Tension in the string $T=20N$
Speed of transverse wave $v=\sqrt{\frac{T}{\mu }}$
$\therefore$ $v=\sqrt{\frac{20}{0.0015}}=116m/s$