# Huygens' Principle for Sound Waves

• FAS1998
In summary: The equation describing the wave equation is a mathematical statement of the fact that the disturbance propagates outwards from its origin at the same speed as the disturbance itself. In other words, the wave equation says that the disturbance travels in a straight line.In summary, when sound travels, the pressure waves push the particles back and fourth in one direction. This causes the sound waves to spread out in all directions.

#### FAS1998

I have a basic understanding of Huygens principle, but I don't quite understand why sound waves follow huygens principle.

When sound travels, particles travel back and fourth in one direction, so how do sound waves end up traveling in all directions after traveling through a slit?

Do sound waves spread out because particles aren't perfectly aligned with one other, and collisions between particles cause the wave to move in directions different than the initial direction of travel. Can huygens principle be derived or is it an empirical law?

Huygens construction assumes a continuum and including particles is outside the model. The spacing between air molecules is much less than the wavelengths involved.

sophiecentaur said:
Huygens construction assumes a continuum and including particles is outside the model. The spacing between air molecules is much less than the wavelengths involved.
I understand that particles aren't part of huygens principle. I'm having trouble understanding why huygens principle can be used to describe oscillating particles.

FAS1998 said:
I understand that particles aren't part of huygens principle. I'm having trouble understanding why huygens principle can be used to describe oscillating particles.
Those two sentences contradict each other.

nasu
sophiecentaur said:
Those two sentences contradict each other.
I'm probably mistaken, but my understanding was that huygens principle doesn't have anything to do with particles, but at the same time sound waves do consist of particles bumping into one another. Although particles are involved in actual sound waves and not in huygens principles, huygens principle can be used to describe sound waves.

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FAS1998 said:
Do sound waves spread out because particles aren't perfectly aligned with one other, and collisions between particles cause the wave to move in directions different than the initial direction of travel.

Hmmm. I think that's part of it. That, plus the the fact that a sound wave is a moving change in the air density. Air molecules are moving around and bouncing off of each other much faster than the speed of sound. If you have a sound wave pass through an opening, the increased density of the air in front of the opening will also cause a slight rise in air pressure, which presses on the lower density air around it, including the side directions. The net effect is that the sound wave diffracts, moving out in all directions from the opening in exactly the way that Huygens principle describes.

Those are my thoughts at least. Someone correct me if I'm mistaken please.

FAS1998
FAS1998 said:
I'm probably mistaken, but my understanding was that huygens principle doesn't have anything to do with particles, but at the same time sound waves do consist of particles bumping into one another. Although particles are involved in actual sound waves and not in huygens principles, huygens principle can be used to describe sound waves.
Pressure, density and temperature are emergent properties that arise when you have a large collection of small particles colliding elastically.

Once you have derived the existence of these properties, you can consider the resulting fluid in terms of those properties and stop worrying about the underlying particles.

Sound is best understood in terms of pressure waves, not in terms of particles.

sophiecentaur
FAS1998 said:
I'm probably mistaken, but my understanding was that huygens principle doesn't have anything to do with particles, but at the same time sound waves do consist of particles bumping into one another. Although particles are involved in actual sound waves and not in huygens principles, huygens principle can be used to describe sound waves.
Despite the fact that the calculations in Huygen's principle involve 'thinking small' (i.e. distances a bit smaller than the wavelength of the waves that are being studied) it is based on Macroscopic ideas and assumes a continuum. It doesn't involve what particles do in any way (which are at a much smaller scale).
Reduce your scale of thought to the microscopic and how gas particles behave and you can predict reliably how large numbers (really really large) will behave and you can assign very straightforward bulk behaviour to most gases.You are then back into the macroscopic world. Huygens is not involved with particles any more than is the functioning of a steam engine, a clock or even a (non solid state) electrical circuit. No one with any sense of the practical would feel the need to take one regime into the other unless there were discrepancies in experimental results. At that point, it becomes necessary to involve the microscopic world - for instance when there is some non-linearity detected. Huygens does not deal with non linearities so there is no 'clash of interests' that you seem to be looking for.

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FAS1998
FAS1998 said:
I have a basic understanding of Huygens principle, but I don't quite understand why sound waves follow huygens principle... Can huygens principle be derived or is it an empirical law?
Huygen's principle follows from a mathematical property of the differential equation (the "wave equation") that in various forms describes just about all wavelike phenomena. The wave equation is linear, meaning that if A and B are solutions of the wave equation (that is, they are functions describing two possible waves) then their sum A+B is also a solution describing some possible wave. A corollary is that we can take any wave and rewrite as a sum of other waves (called "superposition", and doing so is is convenient when the other waves are more mathematically tractable than the original one).
Huygen's principle is just one particular application of superposition: A spherical wave radiating from a point is a solution of the wave equation; therefore more complicated wave forms can be written as a sum of these.

Thus we can say that Huygen's principle is derived from more basic principles if one of those principles is that sound waves obey the wave equation. That in turn can be derived from the basic gas laws and especially the relationship between pressure and volume, and these are derived by applying the methods of statistical mechanics to air viewed as a large collection of very small particles. However, the particleness of the medium disappears when we move from statistical mechanics to the gas laws, so you won't find any explanation that combines Huygen's principle and particles.

FAS1998, sophiecentaur and jbriggs444
FAS1998 said:
I'm probably mistaken, but my understanding was that huygens principle doesn't have anything to do with particles, but at the same time sound waves do consist of particles bumping into one another. Although particles are involved in actual sound waves and not in huygens principles, huygens principle can be used to describe sound waves.
Huygens principle has nothing to do with Magnetic Fields either or Maxwell's Equations but it can be used to construct the path of an EM wave. Huygens is just a more advanced bit of Maths than 1+1=2, which, in its turn, has nothing to do with beans, GBP or points in a rugby game but it can be used to work things out.