A progressive wave is represented by y=12 sin | vedclass

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(C) The given equation of the progressive wave is $y = 12 \sin(5t - 4x)$.Comparing this with the standard wave equation $y = A \sin(\omega t - kx)$,we

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$\frac{\pi}{8} \ cm$

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(C) The given equation of the progressive wave is $y = 12 \sin(5t - 4x)$.Comparing this with the standard wave equation $y = A \sin(\omega t - kx)$,we get the wave number $k = 4 \ rad/cm$.The phase difference $\Delta \phi$ between two points separated by a distance $\Delta x$ is given by the relation $\Delta \phi = k \cdot \Delta x$.We are given the phase difference $\Delta \phi = 90^{\circ} = \frac{\pi}{2} \ rad$.Substituting the values,we have $\frac{\pi}{2} = 4 \cdot \Delta x$.Therefore,$\Delta x = \frac{\pi}{2 	imes 4} = \frac{\pi}{8} \ cm$.

$A$ progressive wave is represented by $y=12 \sin (5 t-4 x) \ cm$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

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