The equation of a travelling wave is $y = 0.07 s i n (12 π x - 500 π t)$ , where the distances are in meter and time t in second. Calculate the wavelength and velocity of the wave.

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Solution

$y = 0.07 sin (12 π x - 500 π t)$
Compare it with standard equation
$y = A sin (w t - k x)$
we get
$w = 500 π r a d / s e c$
and $k = 12 π$
As we know
$k = \frac{2 π}{λ} ∴ λ = \frac{2 π}{k} = \frac{2 π}{12 π} = \frac{1}{6} m$
Also
$w = 2 π f ∴ f = \frac{w}{2 π} = \frac{500 π}{2 π} = 250 H z = f λ = 250 \times \frac{1}{6} = 41.67 m / s e c$

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