An equation of a simple harmonic progressive | vedclass

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Question

(B) The general equation of a simple harmonic progressive wave is $y = A \sin(\omega t - kx)$.Comparing this with the given equation $y = A \sin(100 \

Vedclass · Accepted Answer

$\frac{\pi}{54}$

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(B) The general equation of a simple harmonic progressive wave is $y = A \sin(\omega t - kx)$.Comparing this with the given equation $y = A \sin(100 \pi t - 3x)$,we get the propagation constant $k = 3 	ext{ rad/m}$.The relationship between phase difference $(\Delta \phi)$ and path difference $(\Delta x)$ is given by $\Delta \phi = k \cdot \Delta x$.Given the phase difference $\Delta \phi = \frac{\pi}{18}$.Substituting the values,we get $\frac{\pi}{18} = 3 \cdot \Delta x$.Therefore,the distance between the two particles is $\Delta x = \frac{\pi}{18 \cdot 3} = \frac{\pi}{54} 	ext{ m}$.Thus,the correct option is $B$.

An equation of a simple harmonic progressive wave is given by $y=A \sin (100 \pi t-3 x)$. The distance between two particles having a phase difference of $\frac{\pi}{18}$ in meters is:

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