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  • A wave equation which gives the displacement along the Y direction is given by y= 10^{-4} \sin (60t + 2x), where x and y are in metres and t is time in seconds. This represents a wave

A wave equation which gives the displacement along the Y direction is given by y= 10^{-4} \sin (60t + 2x), where x and y are in metres and t is time in seconds. This represents a wave

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\begin{array}{l} \text { Given: } y=10^{4} \sin (60 t+2 x) \\\\ \Rightarrow k=2, a=10^{4} m, \omega=60 \\\\ \therefore \text { Wavelength } \lambda=\frac{2 \pi}{k} \\\\ =\frac{2 \pi}{2}=\pi \text { meter } \end{array}

\\\therefore \text{Frequency} f=\frac{\omega}{2 \pi}=\frac{60}{2 \pi}=\frac{30}{\pi} H z \\\\ \text{Velocity } v=f \lambda \\\\ or, \ v=\frac{30}{\pi} \times \pi\\\\ v=30 \mathrm{m} / \mathrm{s}

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