A longitudinal wave is represented by y = 10 sin 2 π n t - x λ cm . The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to

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As we know particle velocity, v p = d y d t = 10 × 2 π n × cos 2 π n t - x λ Therefore, v p m a x = 20 π n Now as we know, v = λ n As given in the question, v p m a x = 4 v ⇒ 20 π n = 4 λ n ⇒ λ = 5 π

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