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  4. The equation of a simple harmonic wave is given by y = 5 sin (π /2) (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

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Q. The equation of a simple harmonic wave is given by y = 5 sin $ \frac{\pi }{2} $ (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

MGIMS WardhaMGIMS Wardha 2008

Solution:

The given equation is $ y=5\sin \frac{\pi }{2}(100t-x) $ ...(i) Comparing Eq. (i) with standard wave equation, given by $ y=A\sin (\omega t-kx) $ ...(ii) we have $ \omega =\frac{100\pi }{2}=50\pi $ $ \Rightarrow $ $ \frac{2\pi }{T}=50\pi $ $ \Rightarrow $ $ T=\frac{2\pi }{50\,\pi }=0.04\,s $