Physics - Wave on String Question with Solution | TestHub

The velocity of a transverse wave in a stretched wire is given by $v=\sqrt{\frac{T}{\mu }}$, where $T$ is the tension and $\mu$ is the linear mass density.

The linear mass density $\mu$ can be expressed as $\mu =\pi r^2\rho$, where $r$ is the radius of the wire and $\rho$ is the density of the material.

Substituting $\mu$ into the velocity formula gives $v=\sqrt{\frac{T}{\pi r^2\rho }}=\frac{1}{r}\sqrt{\frac{T}{\pi \rho }}$.

Since both wires are made of copper, their densities $\rho$ are the same. The tension $T$ is also the same for both wires.

Therefore, the velocity $v$ is inversely proportional to the radius $r$, which means $v\propto \frac{1}{r}$.

Since the thinner wire has a smaller radius, the transverse wave will travel faster in the thinner wire.

Answer: travel faster in the thinner wire.