Two wires of radii and , such that . Then which of the following is true?
Transverse wave travels faster in thinner wire
Step 1: Given data
Two wires of radii and , such that .
Step 2: Formula used
The speed of transverse wave in a wire,
where is the tension, is the mass per unit length of the wire.
Step 3: Calculation
The speed of transverse wave in a wire,
Mass per unit length of the wire,
were is the density, l is length, is the area and is the volume.
Now,
Since area and radius are inversely proportional, as the radius of the wire increases, the velocity decreases, and when the radius of the wire decreases, velocity increases.
So the transverse waves travel faster in thinner wires.
Option B is correct.