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

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

Vedclass · Accepted Answer

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

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

When a wave travels in a medium,the particle displacement is 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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