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

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(A) The equation of the harmonic progressive wave is given by: $y = a \sin 2\pi (bt - cx)$.Comparing this with the standard wave equation $y = a \sin

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

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(A) The equation of the harmonic progressive wave is given by: $y = a \sin 2\pi (bt - cx)$.Comparing this with the standard wave equation $y = a \sin (\omega t - kx)$,we have:$\omega = 2\pi b$ and $k = 2\pi c$.The wave velocity $v_w$ is given by $v_w = \frac{\omega}{k} = \frac{2\pi b}{2\pi c} = \frac{b}{c}$.The particle velocity $v_p$ is given by $v_p = \frac{dy}{dt} = a(2\pi b) \cos 2\pi (bt - cx)$.The maximum particle velocity is $v_{p,max} = 2\pi ab$.According to the problem,$v_{p,max} = 2 	imes v_w$.Substituting the values: $2\pi ab = 2 	imes \frac{b}{c}$.Simplifying the equation: $\pi a = \frac{1}{c}$,which gives $c = \frac{1}{\pi a}$.

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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