Question

The extension in a string obeying Hooke's law is x. The speed of a transverse wave in a stretched string is v. If the extension in the string is increased to 1.5x, the speed of the wave will be

• A. 1.22 v
• B. 0.61 v
• C. 1.50 v
• D. 0.75 v

Answer 1

The correct option is A

1.22 v

Speed of a transverse wave in a stretched string $\nu =\sqrt{\frac{T}{\mu }}......\left(i\right)$

Where T is the tension in the string and $\mu$ is mass per unit length.

Since the string obeys Hooke's law, T $\propto$ x ...(ii)

From (i) and (ii) $\nu \propto \sqrt{x}\therefore {\nu }^{{}^{\prime }}=\sqrt{1.5}\nu =1.22\nu$