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(B) The given wave equation is $y = 3 \sin \frac{\pi}{2}(50t - x)$.Expanding this,we get $y = 3 \sin (25\pi t - \frac{\pi}{2}x)$ $...(i)$.The standard

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$\frac{3\pi}{2}$

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(B) The given wave equation is $y = 3 \sin \frac{\pi}{2}(50t - x)$.Expanding this,we get $y = 3 \sin (25\pi t - \frac{\pi}{2}x)$ $...(i)$.The standard wave equation is $y = A \sin (\omega t - kx)$ $...(ii)$.Comparing $(i)$ and $(ii)$,we get angular frequency $\omega = 25\pi 	ext{ rad/s}$ and wave number $k = \frac{\pi}{2} 	ext{ m}^{-1}$.Wave velocity $v = \frac{\omega}{k} = \frac{25\pi}{\pi/2} = 50 	ext{ m/s}$.Particle velocity $v_p = \frac{dy}{dt} = \frac{d}{dt} [3 \sin (25\pi t - \frac{\pi}{2}x)] = 3 	imes 25\pi \cos (25\pi t - \frac{\pi}{2}x) = 75\pi \cos (25\pi t - \frac{\pi}{2}x)$.Maximum particle velocity $(v_p)_{\max} = 75\pi 	ext{ m/s}$.The ratio of maximum particle velocity to wave velocity is $\frac{(v_p)_{\max}}{v} = \frac{75\pi}{50} = \frac{3\pi}{2}$.

The equation of a simple harmonic wave is given by $y = 3 \sin \frac{\pi}{2}(50t - x)$,where $x$ and $y$ are in metres and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is

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