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(B) The given equation of the $SHM$ wave is $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. Expanding this,we get $y = 0.03 \sin (2 \pi t - 0.01 \pi x) \ m$.

Vedclass · Accepted Answer

$\frac{\pi}{4} \ rad$

Vedclass · Answer

(B) The given equation of the $SHM$ wave is $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. Expanding this,we get $y = 0.03 \sin (2 \pi t - 0.01 \pi x) \ m$. Comparing this with the general wave equation $y = a \sin (\omega t - k x)$,we identify the wave number $k$ as $k = 0.01 \pi \ rad/m$. The phase difference $\Delta \phi$ between two particles separated by a distance $\Delta x$ is given by the formula $\Delta \phi = k \Delta x$. Given $\Delta x = 25 \ m$ and $k = 0.01 \pi \ rad/m$,we substitute these values into the formula: $\Delta \phi = (0.01 \pi) 	imes 25 = 0.25 \pi = \frac{\pi}{4} \ rad$. Thus,the phase difference is $\frac{\pi}{4} \ rad$.

$A$ simple harmonic progressive wave is represented as $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. At a given instant of time,the phase difference between two particles $25 \ m$ apart is

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