Energy density E (energy per unit volume ) of the medium ar a distance r from a sound source varies acording to the curve shown in figure. Which of the following are possible?

Options

A. The source may be a point isotropic source
B. if the source is a plane source then the medium particle have damped oscillations
C. if the source is a plane source then power of the sourcee is decresing with time
D. density of the medium decrease with distance `r` from the source

Answer

a., b., d.

Explanation

Due to propagation of a wave the energy density at a point is given by
`E=I//v` Where I is intenssity at that point and v is wave propagation velocity.
it means energy density E is directly propagation to intensity I.
if power emitted by a point source is P then intensity at a distance r from it is equal to
`I=(P)/(4pir^(2)) or Iprop (1)/(r^(2))`
Hence, the shape of the curve between I and r will also be same as that given in figure of the quetion.
hence, option (a) is correct.
if the source is a plane sound source then intensity at every point in front of the source then intensity at every point in front of the source will be same if damping does not take place. but if damping takes place then the amplitude of oscillation of medium particle decrease with distance. hence, the intensity decrease with the distance from the source. in that case, the curve between I and r may have the same shape as shown in the figure given in the equation. hence, option (b) is also correct.
if the source is a plane source, intensity at every point of the source will be the same. but if power if the source is decreasing with time then intensity will also decrease with time. but at an instant, intensity at every point in front of source will be same. therefore, the energy density at every point in front of source will also be same, though it will decrease with time. hence, option (c ) is wrong.
intensity, `I=2pi^(2)n^(2)a^(2)pv`
Since, intensity `I prop p` (density of medium) and density `I` is decrease with distance, therefore, the density `p` also decrease with distance from the source. hence, option (d) is also correct.