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

Answer

C

Explanation

Intensity = Energy/Sec/Area = Power/Area.
From a point source, energy spreads over the surface of a sphere of radius r.
`:.` Intensity `=P/A=P/(4pi r^(2)) prop 1/r^(2)`
But intensity = `("Amplitude")^(2)`
`:. ("Amplitude")^(2) prop 1/r^(2)` or Amplitude `prop 1/r`
At distance 2r, amplitude becomes `A//2`