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(D) The standard equation of a progressive wave is $y = A \sin(2\pi ft - kx)$.Comparing the given equation $y = 6 \sin 2\pi(2t - 0.1x)$ with the stand

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$72$

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(D) The standard equation of a progressive wave is $y = A \sin(2\pi ft - kx)$.Comparing the given equation $y = 6 \sin 2\pi(2t - 0.1x)$ with the standard form,we get the wave number $k = 2\pi 	imes 0.1 = 0.2\pi \ rad/mm$.The relationship between phase difference $\Delta \phi$ and path difference $\Delta x$ is given by $\Delta \phi = k \Delta x$.Given the separation between particles $\Delta x = 2 \ mm$.Substituting the values,$\Delta \phi = (0.2\pi) 	imes 2 = 0.4\pi \ rad$.To convert radians to degrees,multiply by $\frac{180^{\circ}}{\pi}$:$\Delta \phi = 0.4\pi 	imes \frac{180^{\circ}}{\pi} = 0.4 	imes 180^{\circ} = 72^{\circ}$.

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

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