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

Question

Dr. Abubacker · Accepted Answer

(b) The equation for a harmonic progressive wave is $y = 6\sin{2\pi(2t - 0.1x)}$
$\Rightarrow y = 6\sin{(4\pi t - 2\pi 	imes 0.1x)}$ This is of the form
$y = A\sin{(\omega t - kx)}$ where $k = \frac{2\pi}{\lambda}$ $	herefore\lambda = 10mm$
The phase difference for two particles separated by $2\ mm\ is\ \phi = \frac{2\pi}{10} 	imes 2 \Rightarrow \phi = \frac{2\pi}{5} = 72{^\circ}$

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

Explanation

Reviewed by Dr. Abubacker

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