Question

The ratio of radii of two wires is 1:2 and the density of their materials are in the ratio 1:4. If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is:

• A. 1:16
• B. 1:6
• C. 1:4
• D. 4:1

Hint:

To calculate the ratio of the wave speeds, use the relation \( v = \sqrt{\frac{T}{\rho}} \), considering the tension and density of both wires.

Answer 1

The Correct Option is A

The speed of transverse waves is given by \( v = \sqrt{\frac{T}{\rho}} \), where \( T \) is the tension and \( \rho \) is the density. The ratio of the speeds of the waves is the square root of the ratio of the tension to the density. Given the ratio of the radii and densities, we find the ratio of the speeds to be 1:16. Thus, the correct answer is option (1).