MHT CET · Physics · Waves and Sound
Two Cu wires of radii \(R_{1}\) and \(R_{2}\) are such that \(\left(R_{1}>R_{2}\right)\). Then which of the following is true?
- A Transverse wave travels faster in thicker wire
- B Transverse wave travels faster in thinner wire
- C Travels with the same speed in both the wires
- D Does not travel
Answer & Solution
Correct Answer
(B) Transverse wave travels faster in thinner wire
Step-by-step Solution
Detailed explanation
The velocity of a transverse wave
or
\(
\begin{aligned}
v &=\sqrt{\frac{T}{\rho A}} \\
v & \propto \frac{1}{\sqrt{A}} \\
v & \propto \frac{1}{R}
\end{aligned}
\)
Because the velocity of wire depend on the radius. So transverse wave travels faster in thinner wire.
or
\(
\begin{aligned}
v &=\sqrt{\frac{T}{\rho A}} \\
v & \propto \frac{1}{\sqrt{A}} \\
v & \propto \frac{1}{R}
\end{aligned}
\)
Because the velocity of wire depend on the radius. So transverse wave travels faster in thinner wire.
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