A traveling wave is described by the equation $y (x, t) = [0.05 sin (8 x - 4 t)]$ m
The velocity of the wave is [All the quantities are in SI unit]

Question

A traveling wave is described by the equation y ( x , t ) = [ 0.05 sin ( 8 x − 4 t )] m The velocity of the wave is [All the quantities are in SI unit]

TestHub · Accepted Answer

The given equation of the traveling wave is $y (x, t) = 0.05 sin (8 x - 4 t)$ m.

Comparing this with the standard equation of a traveling wave $y (x, t) = A sin (k x - ω t)$ , we get:

$k = 8 m^{- 1}$

$ω = 4 rad s^{- 1}$

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

Substituting the values, we get:

$v = \frac{4}{8} = 0.5 ms^{- 1}$

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