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Question

A longitudinal wave is represented by x=x0sin2π(ntπλ). The maximum particle velocity will be four times the wave velocity if

A
λ=πx04
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B
λ=2πx0
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C
λ=πx02
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D
λ=4πx0
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Solution

The correct option is C λ=πx02


We have the longitudinal wave given by

x=x0sin[2π(ntxλ)]

=x0sin(2πnt2πλx)

The maximum particle velocity

=Aω=x0(2πn)

The wave velocity =nλ

Here we compare the given equation with the equation x=x0sin(ωt±kx)

From the question, 2πnx0=4nλ

λ=π2x0


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