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Time Period Independent of Amplitude

Two Cu wires ...

Question

Two Cu wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$ . Then which of the following is true ?

Transverse wave travels faster in thicker wire

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Transverse wave travels faster in thinner wire

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Travels with the same speed in both the wires

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Does not travel

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Solution

The correct option is B Transverse wave travels faster in thinner wire
Speed of transverse wave in a wire is given as-
$v = \sqrt{\frac{T}{μ}}$
where $μ$ is the mass per unit length of wire.
$μ = \frac{m}{l} = \frac{m}{V} A = ρ A$
Hence $v = \sqrt{\frac{T}{ρ A}}$
$\propto \frac{1}{\sqrt{A}}$
Thus speed is higher for thinner wire.

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

The correct option is B Transverse wave travels faster in thinner wireSpeed of transverse wave in a wire is given as-v=√Tμwhere μ is the mass per unit length of wire.μ=ml=mVA=ρAHence v=√TρA∝1√AThus speed is higher for thinner wire.

Two Cu wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$ . Then which of the following is true ?