Question

A transverse wave is travelling with velocity \( V \) through a metal wire of length \( L \) and density \( \rho \). The tensile stress in the wire is

• A. \( V \rho^2 \)
• B. \( \frac{V^2}{\rho} \)
• C. \( \frac{\rho}{V^2} \)
• D. \( V^2 \rho \)

Hint:

In wave motion on a stretched string, the wave velocity is related to the tensile stress and density by \( V = \sqrt{\frac{T}{\rho}} \). Rearranging gives \( T = \rho V^2 \).

Answer 1

The Correct Option is D

Step 1: Understanding the relationship between wave velocity and stress.
The wave velocity \( V \) on a stretched string is given by: \[ V = \sqrt{\frac{T}{\rho}} \] Where: - \( T \) is the tensile stress, - \( \rho \) is the density. Rearranging the equation for stress \( T \), we get: \[ T = \rho V^2 \] Thus, the correct answer is (D) \( V^2 \rho \).