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(D) The standard equation of a simple harmonic progressive wave is $y = A \sin(kx - \omega t)$.Comparing this with the given equation $y = 8 \sin(2\pi

Vedclass · Accepted Answer

$72$

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(D) The standard equation of a simple harmonic progressive wave is $y = A \sin(kx - \omega t)$.Comparing this with the given equation $y = 8 \sin(2\pi(0.1x - 2t)) = 8 \sin(0.2\pi x - 4\pi t)$,we get the wave number $k = 0.2\pi \, rad/cm$.The phase difference $\Delta \phi$ between two particles separated by a distance $\Delta x$ is given by $\Delta \phi = k \Delta x$.Given $\Delta x = 2.0 \, cm$,we have $\Delta \phi = (0.2\pi) 	imes 2.0 = 0.4\pi \, radians$.To convert radians to degrees,we multiply by $\frac{180^o}{\pi}$:$\Delta \phi = 0.4\pi 	imes \frac{180^o}{\pi} = 0.4 	imes 180^o = 72^o$.

$A$ simple harmonic progressive wave is represented by the equation $y = 8\sin 2\pi (0.1x - 2t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. At any instant,the phase difference between two particles separated by $2.0 \, cm$ in the $x$-direction is ..... $^o$.

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