A progressive wave is given by Y = 12 sin (5t | vedclass

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(B) The given equation of the progressive wave is $y = 12 \sin (5t - 4x)$.The standard form of a progressive wave is $y = A \sin (\omega t - kx)$,wher

Vedclass · Accepted Answer

$\frac{\pi}{8}$

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(B) The given equation of the progressive wave is $y = 12 \sin (5t - 4x)$.The standard form of a progressive wave is $y = A \sin (\omega t - kx)$,where $k = \frac{2\pi}{\lambda}$.Comparing the given equation with the standard form,we get the wave number $k = 4$.The relationship between phase difference $(\Delta \phi)$ and path difference $(\Delta x)$ is given by $\Delta \phi = k \cdot \Delta x$.Given phase difference $\Delta \phi = 90^{\circ} = \frac{\pi}{2}$ radians.Substituting the values: $\frac{\pi}{2} = 4 \cdot \Delta x$.Therefore,$\Delta x = \frac{\pi}{2 \cdot 4} = \frac{\pi}{8}$.

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

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