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(B) The given equation of the harmonic progressive wave is $y=A \sin (100 \pi t+3 x)$.Comparing this with the standard wave equation $y=A \sin (\omega

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$\frac{\pi}{9} \ m$

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(B) The given equation of the harmonic progressive wave is $y=A \sin (100 \pi t+3 x)$.Comparing this with the standard wave equation $y=A \sin (\omega t+kx)$,we get the wave number $k=3 \ m^{-1}$.The relationship between wave number $k$ and wavelength $\lambda$ is $k = \frac{2 \pi}{\lambda}$.Substituting the value of $k$,we have $3 = \frac{2 \pi}{\lambda}$,which gives $\lambda = \frac{2 \pi}{3} \ m$.The path difference $\Delta x$ and phase difference $\Delta \phi$ are related by the formula $\Delta x = \frac{\lambda}{2 \pi} 	imes \Delta \phi$.Given the phase difference $\Delta \phi = \frac{\pi}{3}$ radian.Substituting the values,we get $\Delta x = \frac{2 \pi / 3}{2 \pi} 	imes \frac{\pi}{3} = \frac{1}{3} 	imes \frac{\pi}{3} = \frac{\pi}{9} \ m$.

$A$ simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

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