The equation for spherical progressive wave is (where r is the di… - Vidyadip

MCQ

The equation for spherical progressive wave is (where $r$ is the distance from the source)

A
$y = a\sin (\omega t - kx)$
B
$y = \frac{a}{{\sqrt r }}\sin (\omega t - kx)$
C
$y = \frac{a}{2}\sin (\omega t - kx)$
✓
$y = \frac{a}{r}\sin (\omega t - kx)$

✓

Answer

Correct option: D.

$y = \frac{a}{r}\sin (\omega t - kx)$

d
(d) For spherical wave intensity $(I) \propto \frac{1}{{{{({\rm{Distance}}\,r)}^2}}}$

also $I \propto {a^2}$ ==> $a \propto \frac{1}{r}$. Hence equation of a cylindrical wave is $y = \frac{1}{r}\sin (\omega t - kx)$

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