The amplitude of a wave at a distance r from | vedclass

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Question

(C) For a spherical wave originating from a point source,the intensity $I$ is inversely proportional to the square of the distance $r$,i.e.,$I \propto

Vedclass · Accepted Answer

$A/2$

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(C) For a spherical wave originating from a point source,the intensity $I$ is inversely proportional to the square of the distance $r$,i.e.,$I \propto 1/r^2$.Since the intensity $I$ is also proportional to the square of the amplitude $A$ $(I \propto A^2)$,we can write $A^2 \propto 1/r^2$.Taking the square root on both sides,we get $A \propto 1/r$.Therefore,the ratio of amplitudes at two different distances is given by $A_1/A_2 = r_2/r_1$.Given $r_1 = r$,$A_1 = A$,and $r_2 = 2r$,we substitute these values:$A/A_2 = (2r)/r = 2$.Solving for $A_2$,we get $A_2 = A/2$.

The amplitude of a wave at a distance $r$ from a point source is $A$. What will be the amplitude at a distance $2r$ from the source?

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