Do Spherical Waves from Point Sources Transform into Plane Waves?

[TheEdge]

Hi guys,

Let's assume I have a point source in a free field. Now, correct me if I'm wrong on any of the following points:

• As the spherical waves spread out from the point source, they will tend towards plane waves.

• Since planes waves lose less intensity with distance than spherical waves (due to wavefront area not increasing), the rate at which the intensity falls will decrease with distance.

• A graph will look like the attachment. The black line is for an ideal point source where the waves stay spherical with distance, the blue line for the situation I've described.

Thanks,
Stewart

 

[OlderDan]

Hi guys,

Let's assume I have a point source in a free field. Now, correct me if I'm wrong on any of the following points:

• As the spherical waves spread out from the point source, they will tend towards plane waves.

• Since planes waves lose less intensity with distance than spherical waves (due to wavefront area not increasing), the rate at which the intensity falls will decrease with distance.

• A graph will look like the attachment. The black line is for an ideal point source where the waves stay spherical with distance, the blue line for the situation I've described.

Thanks,
Stewart

Your black line already accounts for the reduced rate of intensity loss. If there are no energy losses, the intensity (energy per unit area) will be inversely proportional to area, which is proportional to distance^2

I=K/r^2

At some reference distance say 1m, the intensity is Io

Io = K/(1m)^2

So

I/Io = (r/1m)^(-2)

Taking log of both sides

log (I/Io) = -2log(r/1m)

This is what your black line is showing

The rate of intensity loss with increasing distance is the derivative of intensity wrt r

dI/dr = K(-2)/r^3

This is a rapidly decreasing function of r. There is no reason to expect a slower rate.