What will be the effect on the speed of transverse waves on a string if the tension in the string remains constant but the diameter of the string doubles?

Explanation

The speed of transverse waves on a string is given by the formula v = √(T/μ), where T is the tension and μ is the linear density (mass per unit length) of the string. When the tension remains constant and the diameter of the string doubles, the cross-sectional area (and consequently the mass of the string per unit length) increases by a factor of four, since area is proportional to the square of the diameter. This results in the linear density increasing by four times.Since v = 1/√μ, a fourfold increase in the linear density results in the speed of the wave being halved. Therefore, the correct answer is that the speed becomes half. The other options are incorrect because they do not account for the change in linear density appropriately.