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(A) Given the displacement of a particle in the wave is $y = A \sin (\omega t - k x)$.The particle velocity $v_p$ is defined as the rate of change of

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$A \omega$

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(A) Given the displacement of a particle in the wave is $y = A \sin (\omega t - k x)$.The particle velocity $v_p$ is defined as the rate of change of displacement with respect to time:$v_p = \frac{dy}{dt}$Differentiating the displacement equation with respect to $t$:$v_p = \frac{d}{dt} [A \sin (\omega t - k x)] = A \omega \cos (\omega t - k x)$For the maximum particle velocity,the cosine term must be at its maximum value,which is $1$:$v_{p, 	ext{max}} = A \omega (1) = A \omega$Thus,the maximum particle velocity is $A \omega$.

$A$ wave travelling along a string is described by the equation $y = A \sin (\omega t - k x)$. The maximum particle velocity is:

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