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  4. A plane progressive wave is given by y = 2 cos 6.284 (330 t - x). What is period of the wave ?

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Q. A plane progressive wave is given by $y = 2 \,cos\, 6.284 (330\, t - x)$. What is period of the wave ?

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Solution:

We have the progressive wave given by
$y=2 \cos 6.284(330\, t-x)=2 \cos 2 \pi(330\, t-x)$
$=2 \cos (2 \pi \times 330\, t-2 \pi x), $
$\omega=2 \pi \times 330$
and time period $T=\frac{2 \pi}{\omega}=\frac{1}{330} s$.