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I am having trouble understanding electromagnetic radiation (or waves in general, be it EM or sound). If I have a 1 Watt speaker, is it infinitely divided and spread out so that everyone in every direction around the speaker can hear it?

I do not believe they have "height", to reach more than one person at once, but if they did they would probably collide at one point. How do sound waves travel "backwards" (i.e. you are behind a speaker), are they scattered by air particles or itself so that people behind could hear it (at reduced amplitude)?

I am just unsure how to wrap my head around it.

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Hi John, and welcome to Physics Stack Exchange! Sound waves aren't an example of electromagnetic radiation. Light waves and radio waves are electromagnetic, but not sound. To be clear: are you asking a question about all waves, or only sound? In the latter case do you specifically mean sound waves emitted from a (directional) speaker? –  David Z Feb 12 '12 at 7:44
    
My mistake about sound waves, however both energy (i.e. 1 Watt speaker, or 1 Watt RF transmitter, any "wave" such as that.) And affirmative, I mean a directional speaker. –  John Q. Feb 12 '12 at 7:46
    
And thank you for the warm welcome. :) –  John Q. Feb 12 '12 at 7:48
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2 Answers

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Infinitely divided

First thing, EM waves cannot be infinitely divided (not too sure about sound waves, there is some concept of phonons). EM waves come in finite packets known as photons. But this is irrelevant to the main problem. Yes, in generay, for a source of sound/light that has no directional preference, the waves will be uniformly distributed, For a speaker, not so much. But the waves will be distributed in all directions, just not uniformly. We'll see.


Now, the waves need not be radiated everywhere at once. Normal antennae radiate in all directions, but there are directional antennae as well, which radiate mainly forwards.

Diffraction

Now, comparing your exeriences with light against sound is a bad idea, because light has a small wavelength (in micrometers), and sound has wavelengths in meters. What does this change? It changes the extent of diffraction. Diffraction is the bending of waves around obstacles, and is more effective for larger wavelengths. See the diagrams here (these are for a source emitting in all directions, though). All waves can bend around corners, but we only notice this for sound, as it has a large wavelength.

Explanation with diffraction

Now, how does this explain hearing someone from behind them? There are two ways of looking at this. One way (which I don't like), is by just saying that the sound diffracts around your head. After all, the head is a type of obstacle (One can also consider air particles). Remember that sound intensity is drastically decreased when you stand behind a speaker, so this seems to explain the phenomenon.

Explanation without diffraction

I like to explain this in the following manner. (If you do not know the mechanism of sound wave propagation, first read this and understand what comressions/rarefactions are). Note that I'm not sure if this is an accepted explanation, its just much easier to "wrap your head around". And it seems to work.

I shall refer to this diagram (apologies for the sloppyness) for this part of my answer: Sound

In (A), there is a person speaking. He generates pressure oscillations (i.e., sound). In the diagram, I have denoted compressions by black lines and rarefactions by yellow. There shouldn't be that large a size difference, but I'm rather lazy. I've also not made the sound waves propagate outwards as the diagrams progress, due to the aforementioned laziness.

Now, the air behind the person is at normal pressure. So, it will be sucked into the rarefactions, and similarly, the compressions will be sucked into this region. See the arrows in (B). Now, Due to the exchange of air, the pressure of an area next to a rarefaction will decrease, and that of one near a compression will increase (C). Finally, we get a (slightly weaker) set of compressions and rarefactions behind the speaker (It happens on the top, too, but I haven't drawn that). One can easily see that this process will continue, and the sound will finally go in all directions, with varying intensity.

???

I do not believe they have "height", to reach more than one person at once, but if they did they would probably collide at one point. Could you please elaborate this? I don't understand what exactly you're asking. If you're talking about sound from a speaker, they will reach everyone nearby. I don't know what you mean by "height".

Most probably, this explanation will boil down to being diffraction in the end, but I personally feel that it is easier to understand than diffraction (which is more of a 'it just is' phenomena till you learn waves in proper)


Conclusion

Sound is able to diffract extensively. Thus it can do all sorts of things that we don't observe with light, like bending around obstacles. Sound CAN be heard from behind a source, but the intensity will be less. This can be explained both by diffraction and the fundamental pressure difference way.

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Thank you, this is a lot easier to wrap my head around than I thought. By height, I meant physical height of the waves colliding against each other, which could have been a problem if it were infinitely in every direction. –  John Q. Feb 12 '12 at 21:20
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I guess you mean amplitude of the waves. That doesn't really become an issue, even if waves aren't quantised. When waves collide with surfaces, we take the area of the surface into account as well, so the 'height' of the wave hitting the surface is not zero, but rather a fraction of the amplitude of the original wave (the fraction is determined by solid angles). When waves collide with each other, they interfere. The amplitude is involved here, but it does not create a problem. See en.wikipedia.org/wiki/Interference_(wave_propagation) –  Manishearth Feb 13 '12 at 5:54
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Electromagnetic or acoustic waves cannot be "infinitely divided", but the minimal "portions" of the waves (quanta - photons or phonons) typically have very low energy. Radiation from an acoustic speaker or an electromagnetic antenna propagates in all directions, but if the speaker or the antenna is directional, the so called intensity of radiation strongly depends on the direction. In some directions the intensity may be extremely small. Propagation of radiation, including backward propagation (say, behind the speaker), is determined by so called diffraction (you may wish to google this term).

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