Equation of a progressive wave y = a sin ( 400 π t − 0.85 π x ) then its velocity will be :

Question

Equation of a progressive wave y = a sin ( 400 π t − 0.85 π x ​ ) then its velocity will be :

TestHub · Accepted Answer

The standard equation for a progressive wave is $y = A sin (ω t - k x)$ .

Comparing this with the given equation $y = a sin (400 π t - \frac{π x}{0.85})$ , we find $ω = 400 π$ rad/s and $k = \frac{π}{0.85}$ rad/m.

The wave velocity $v$ is given by $v = \frac{ω}{k}$ .

$v = \frac{400 π}{\frac{π}{0.85}} = 400 \times 0.85 = 340 m / s$

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