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.

 

[kyle8921]

Hello Stewart,

You are correct in your understanding of how waves from a point source behave. As you mentioned, the intensity of the waves will decrease with distance, but the rate at which it decreases will be slower for plane waves compared to spherical waves. This is due to the fact that the wavefront area does not increase for plane waves, resulting in less energy being spread out over a larger area. This is known as the inverse square law, where the intensity of a wave is inversely proportional to the square of the distance from the source.

The graph you have provided is a good representation of how the intensity of waves from a point source changes with distance. The black line represents an ideal point source where the wavefronts remain spherical, resulting in a faster decrease in intensity with distance. The blue line, on the other hand, represents the situation you described where the wavefronts tend towards plane waves, resulting in a slower decrease in intensity.

It is important to note that real acoustical sources may not behave exactly like an ideal point source. Factors such as the size and shape of the source, as well as the surrounding environment, can affect how the waves propagate. However, the concept of the inverse square law still applies and understanding the behavior of waves from a point source is crucial in many areas of acoustics.

I hope this helps clarify your understanding of real acoustical sources. Keep up the good thinking!

Best,