Topic: Other
Concepts: Standing waves, Tensile strength, Wave speed in string

Solution:

Recall the wavelength of the fundamental mode is given by $\lambda=2L$. The fundamental frequency $f$ is then

Since the speed of a wave in a string is given by

we have

since we are considering strings of the same length.

In terms of the radius $r$, the maximum possible tension $T \propto r^2$ since it is determined by the tensile strength (force per area) of the material. The mass $M \propto r^2$ since the volume of the string is proportional to its area. Then

so the frequency is independent of radius. Thus, the answer is A.