When a wave travels in a medium,the particle | vedclass

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(A) The displacement equation is given by $y = a \sin(2\pi bt - 2\pi cx)$.Comparing this with the standard wave equation $y = A \sin(\omega t - kx)$,w

Vedclass · Accepted Answer

$c = \frac{1}{\pi a}$

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(A) The displacement equation is given by $y = a \sin(2\pi bt - 2\pi cx)$.Comparing this with the standard wave equation $y = A \sin(\omega t - kx)$,we get:Amplitude $A = a$,angular frequency $\omega = 2\pi b$,and wave number $k = 2\pi c$.The maximum particle velocity is $V_{\max(P)} = A\omega = a(2\pi b) = 2\pi ab$.The wave velocity is $v = \frac{\omega}{k} = \frac{2\pi b}{2\pi c} = \frac{b}{c}$.According to the problem,the maximum particle velocity is twice the wave velocity:$V_{\max(P)} = 2v$$2\pi ab = 2 \left( \frac{b}{c} \right)$$\pi a = \frac{1}{c}$$c = \frac{1}{\pi a}$.

When a wave travels in a medium,the particle displacements are given by $y = a \sin 2\pi (bt - cx)$ where $a, b,$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

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