Question

Two strings of equal length are stretched out with equal tension. The mass of the second string is four times the mass of first string. If a wave travels down the first string with velocity $v$. Find out the velocity of a wave on the second string?

• A. $\frac{1}{4}v$
• B. $\frac{1}{\sqrt{2}}v$
• C. $v$
• D. $2v$
• E. $4v$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}v$

Velocity of wave in stretched string is given by $v=\sqrt{T/m}$ where $T=$ tension in string and $m=$ mass/unit length given tension is equal in both strings ,

Now, velocity of wave in first stretched string $v=\sqrt{T/m}$

velocity of wave in second stretched string $v_2=\sqrt{T/2m}$

therefore, $v_2=\frac{1}{\sqrt{2}}\sqrt{T/m}=\frac{1}{\sqrt{2}}v$