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Q.
The equation of a wave is $y = 5\, \sin (\frac{t}{0.04} - \frac{x}{4})$ ; where, $x$ is in $cm$ and $t$ is in second. The maximum velocity of the wave will be
Equation of wave $y = 5\, \sin (\frac{t}{0.04} - \frac{x}{4})$
The standard equation of a wave in the given form is
$y = a \sin ( \omega t - \frac{2 \pi x}{\lambda})$
Comparing the given equation with the standard equation, we get
$a = 5$ and $\omega = \frac{1}{0.04} = 25$
Therefore, maximum velocity of particles of the medium.
$v_{max} = a \omega = 5 \times 25 = 125 \, cm\,s^{-1} = 1.25 \, ms^{-1}$