The equation of a simple harmonic progressive | vedclass

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(C) The given wave equation is $Y = a \sin(2 \pi b t - 2 \pi c x)$.Comparing this with the standard wave equation $Y = A \sin(\omega t - k x)$,we get

Vedclass · Accepted Answer

$c = \frac{1}{\pi a}$

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(C) The given wave equation is $Y = a \sin(2 \pi b t - 2 \pi c x)$.Comparing this with the standard wave equation $Y = A \sin(\omega t - k x)$,we get angular frequency $\omega = 2 \pi b$ and wave number $k = 2 \pi c$.The maximum particle velocity is given by $(V_{max})_p = \omega A = (2 \pi b) a$.The wave velocity is given by $V_w = \frac{\omega}{k} = \frac{2 \pi b}{2 \pi c} = \frac{b}{c}$.According to the problem,the maximum particle velocity is twice the wave velocity:$(V_{max})_p = 2 V_w$.Substituting the values: $2 \pi b a = 2 \left( \frac{b}{c} \right)$.Dividing both sides by $2b$,we get $\pi a = \frac{1}{c}$,which implies $c = \frac{1}{\pi a}$.

The equation of a simple harmonic progressive wave is given by $Y = a \sin 2 \pi (b t - c x)$. The maximum particle velocity will be twice the wave velocity if:

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