Question

A string of length $2x$ is stretched by $0.1x$ and the velocity of a transverse wave along it is $v$ . When it is stretched by $0.4x$ , the velocity of the wave is

• A. $\sqrt{\frac{5}{6}}v$
• B. $\sqrt{\frac{11}{7}}v$
• C. $\sqrt{\frac{32}{7}}v$
• D. $\sqrt{\frac{27}{6}}v$

Answer 1

Answer: (C)

Wave speed $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{TL}{M}}$
$\frac{v_2}{v_1}=\sqrt{\frac{T_2{L}_2}{T_1{L}_1}}=\sqrt{\frac{\left(k{x}_2\right)\left(l_0+x_2\right)}{\left(k{x}_1\right)\left(l_0+x_1\right)}}$
$\frac{v_2}{v_1}=\sqrt{\frac{\left(0.4x\right)\left(2x+0.4x\right)}{\left(0.1x\right)\left(2x+0.1x\right)}}$
$\frac{v_2}{v}=\sqrt{\frac{4\left(24\right)}{\left(1\right)\left(21\right)}}=\sqrt{\frac{32}{7}}$
$v_2=\sqrt{\frac{32}{7}}v$