If the amplitude of a wave at a distance `r` from a point source is `A`, the amplitude at a distance `2 r` will be

Options

A. 2A
B. A
C. `(A)/(2)`
D. `(A)/(4)`

Answer

C

Explanation

The intensity `(I) prop ("Amplitude "A)^(2)`
and Intensity `(I) prop (1)/(r^(2))`(as per inverse square law)
`:. A^(2) prop (1)/(r^(2)) or A prop (1)/(r)`
`:. (A_(2))/(A_(1)) = (r_(1))/(r_(2)) = (r)/(2r) = (1)/(2)`
`:. A_(2) = (A_(1))/(2) or A_(2) = (A)/(2)`
Note: For a plane progressive wave, the amplitude does not vary with distance. For a spherical wave `A prop (1)/(r)` and for a cylindrical wave `A prop (1)/(sqrtr)`