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  4. Equation of a progressive wave is y=a sin ( 400π t-(π x/0.85) ), then its velocity will be:

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Q. Equation of a progressive wave is $ y=a\,\sin \left( 400\pi t-\frac{\pi x}{0.85} \right), $ then its velocity will be:

Rajasthan PMTRajasthan PMT 2000Waves

Solution:

Equation of wave is
$y=a \sin \left(400 \pi t-\frac{\pi x}{0.85}\right)$
Comparing this equation with
$y =a \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right) $
$\omega =400 \pi $
$2 \pi n =400 \pi \Rightarrow n=200 $
$\lambda =0.85 \times 2=1.7$
Velocity $v=n \lambda=1.7 \times 200=340\, m / s$