A plane progressive wave is represented by the equation $y = 0.1\sin \left( {200\pi t - \frac{{20\pi x}}{{17}}} \right)$ where y is displacement in $m$, $ t$ in second and $x$ is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are
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(a) Comparing the given equation with standard equation
We get $\omega = 2\pi n = 200\pi $ ==> $ n = 100 Hz$
$k = \frac{{20\pi }}{{17}}$ ==> $\lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{20\pi /17}} = 1.7\,m$
and $v = \frac{\omega }{k} = \frac{{200\,\pi }}{{20\pi /17}} = 170\,m/s.$
We get $\omega = 2\pi n = 200\pi $ ==> $ n = 100 Hz$
$k = \frac{{20\pi }}{{17}}$ ==> $\lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{20\pi /17}} = 1.7\,m$
and $v = \frac{\omega }{k} = \frac{{200\,\pi }}{{20\pi /17}} = 170\,m/s.$
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