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The maximum particle velocity is 4 times the wave velocity of a progressive wave. If the amplitude of the particle is ‘A’. The phase difference between the two particles separated by a distance of ‘X’ is $\frac{N X}{A}$ then N is

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answer is C.

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Detailed Solution

We know

$V_{\max} = A ω & V_{wave} = fλ,$

Given

$V_{\max} = 4 V_{wave} (given)$

$\Rightarrow Aω = 4 fλ$

$\Rightarrow A (2 πf) = 4 fλ \Rightarrow \frac{2 π}{λ} = \frac{4}{A}$

Phase difference,

$ϕ = \frac{2 π}{λ} X \Rightarrow ϕ = \frac{4}{A} X$

$∴ N = 4$

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