A simple harmonic progressive wave is represented by the equation… - Vidyadip

MCQ

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 ..... $^o$

A
$18$
B
$36$
C
$54$
✓
$72$

✓

Answer

Correct option: D.

$72$

d
(d) From the given equation $k = 0.2\pi $
==>$\frac{{2\pi }}{\lambda } = 0.2\pi \Rightarrow \lambda = 10\,cm$
$\Delta \phi = \frac{{2\pi }}{\lambda }\,\Delta x = \frac{{2\pi }}{{10}} \times 2 = \frac{{2\pi }}{5} = {72^o}\,$

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