Question

A wave is travelling on a string with velocity $V_0$. If the mass of the string is doubled and length is tripled, what is the new velocity for the given Tension in the string?

• A. $\left(\frac{3}{2}\right)V_0$
• B. $6V_0$
• C. $\sqrt{\frac{3}{2}}{V}_0$
• D. $\sqrt{6}{V}_0$

Answer 1

The correct option is C $\sqrt{\frac{3}{2}}{V}_0$

We know that the velocity of a wave $V_m$ in a string is given by,

$V_m=\sqrt{\frac{T}{\mu }}=V_0$

$\mu =\frac{\text{mass of string}}{\text{Length of string}}=\frac{m}{l}$

After change,

${\mu }^{\prime }=\frac{2m}{3l}=\frac{2}{3}\mu$

$\Rightarrow V_m^{\prime }=\sqrt{\frac{T}{{\mu }^{\prime }}}$

$\Rightarrow V_m^{\prime }=\sqrt{\frac{T}{\mu }}\times \sqrt{\frac{3}{2}}$

$\Rightarrow V_m^{\prime }=\sqrt{\frac{3}{2}}{V}_0$

Hence, option $\left(C\right)$ is correct

Why this question ? This question gives you understanding about wave velocity on a string and its dependency on other quality.