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On the topic of sound waves, my textbook says in one place,

Sound waves constitute alternate compressions and rarefactions, which are produced by vibrations of the source, oscillating in a simple harmonic fashion.

In another place, it says,

The sound waves are, in general, three dimensional waves. There exist spherical layers of the medium (on which sound propagates) on which pressure at various elements have the same phase at a given instant.

How do the two statements concur? What I understand is that the vibrations (in a particular direction) produce compressions and rarefactions in that direction, and hence sound travels along that direction.

In that case, When the source is vibrating in a simple harmonic manner in a particular direction, how can spherical wavefronts be produced?

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    $\begingroup$ The text says "there exists", that is, it is possible to produce such spherical waves. It does not say that that vibrations described in the first paragraph will produce such a wave. $\endgroup$
    – garyp
    Commented Jun 19, 2021 at 3:46
  • $\begingroup$ I understand, but let's take the example of a tuning fork. The arms of teh fork vibrate in a simple harmonic manner. So, are the sound waves produced in this case, spherical in nature? $\endgroup$
    – Nilabja
    Commented Jun 19, 2021 at 3:48
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    $\begingroup$ Nearby to the fork, no. As you move further and further away, the waves become more and more spherical. The pattern never becomes strictly spherical, but it does become indistinguishable from a sphere due to the limited sensitivity of whatever equipment that you are using. Note that the phase fronts will be spherical, but the amplitude distribution will not be. $\endgroup$
    – garyp
    Commented Jun 19, 2021 at 14:24

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When the source is vibrating in a simple harmonic manner in a particular direction, how can spherical wavefronts be produced?

Most speakers cannot produce much directionality to the sounds that come from them. They are so small compared to the wavelengths produced that diffraction effects are very large. Directionality comes more from the cabinet or enclosure that they are mounted in.

So a real speaker will have higher power in some directions rather than others, but the idea that it produces spherical waves (in air) is going to be correct.

If you think about having a conversation with a person, yes it will be louder when the person is facing you, but in a quiet location you will have no problems hearing them if they are facing away. This true even when you are not in room with lots of reflections. Even in an open space, the sound will propagate in all directions.

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