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Question

Two Cu wires of radii R1 and R2, such that (R1>R2). Then which of the following is true?


A

Transverse wave travels faster in thicker wire.

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B

Transverse wave travels faster in thinner wire

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C

Travels with the same speed in both the wires.

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D

Does not travel.

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Solution

The correct option is B

Transverse wave travels faster in thinner wire


Step 1: Given data

Two Cu wires of radii R1 and R2, such that (R1>R2).

Step 2: Formula used

The speed of transverse wave in a wire,

v=Tμ

where T is the tension, μ is the mass per unit length of the wire.

Step 3: Calculation

The speed of transverse wave in a wire,

v=Tμ

Mass per unit length of the wire,

μ=mlμ=mVAμ=ρA

were ρ is the density, l is length, A is the area and V is the volume.

Now,

v=Tμv=TρAμ=ρAv1AA=πr2v1πr2v1r

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.


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