The equation of a simple harmonic wave is given by $y=3 \sin \frac{\pi}{2}(50 t-x)$ 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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Aicharya · Accepted Answer

We know that $\begin{aligned} & v_{	ext {max }}=a \omega \ & v=n \lambda \ & 	herefore \quad \frac{v_{\max }}{v}=\frac{a \omega}{n \lambda} \ & =\frac{a(2 \pi n)}{n \pi}=\frac{2 \pi a}{\lambda} \ & =\frac{2 \pi a}{2 \pi / k} \ & =k a=\frac{\pi}{2} 	imes 3 \ & =\frac{3 \pi}{2} \ & \end{aligned}$ ~

The equation of a simple harmonic wave is given by $y=3 \sin \frac{\pi}{2}(50 t-x)$ where $x$ and $y$ are in…

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