A wave equation which gives the displacement along the $Y$ direction is given by the equation $y = {10^4}\sin (60t + 2x)$, where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave
IIT 1982, Medium
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(d) On comparing the given equation with
$y = a\sin (\omega \,t + kx),$ it is clear that wave is travelling in negative $x-$direction.
It's amplitude $a = 10^4\, m$ and $\omega = 60, k = 2.$
Hence frequency $n = \frac{\omega }{{2\pi }} = \frac{{60}}{{2\pi }} = \frac{{30}}{\pi }Hz$
$k = \frac{{2\pi }}{\lambda } = 2$ ==> $\lambda = \pi \,m$ and $v = \frac{\omega }{k} = \frac{{60}}{2} = 30\,m/s$
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