Waves traveling in all directions

[member 529879]

I'm confused about why waves travel in all directions. If an object such as a string is vibrating it is pushing air around it back in forth which creates sound waves. But why do they not only travel in the direction that the string is vibrating in?

 

[A.T.]

http://en.wikipedia.org/wiki/Huygens–Fresnel_principle

 

[USeptim]

In a field theory, its propagation equations tells you how the field propagates, and the propagation can be in diferent directions than the source direction of motion.

For example, a charged particle moving in the X axis will create a magnetic field outside the X axis. In this case the Maxwell equations (and the solution for this case), would show the magnetic field at every point of the space.

 

[Drakkith]

In something such as a sound wave it is easy to understand. The air is made up of molecules and atoms. These can impact each other at many different angles and over time transfer the energy/momentum of the string's motion outwards in all directions. However, this does not work for something like an electromagnetic wave. In that case you need to look at the huygens-fresnel principle, linked above, which applies to all kinds of waves.

Basically the principle boils down to the fact that a disturbance in a medium or field would rather propagate outwards in all directions if it capable of doing so. If we had an infinitely small. point-like oscillator, this would indeed be the case, and you'd get a perfectly spherical wavefront. But with real, extended oscillators, such as a vibrating string, the disturbances from different parts of the medium/field interfere with each other and prevent themselves from spreading out. On the boundaries of the oscillator (and resulting disturbance), the disturbance can indeed spread outwards since it lacks something to interfere with.

The Huygens-Fresnel principle describes all of this by taking a wavefront (the disturbance) and modeling it as a sum of an infinite amount of 'wavelets', which are waves generated by a point oscillator. The interference of all these wavelets gives you the resulting wavefront.

Your original question, which I take to be "why does it spread out in the first place", is mostly just an observed fact. When the oscillator is very small compared to the wavelength of the oscillation, the resulting wave spreads out much better than when the oscillator is very large compared to the wavelength of the oscillation. In other words, the smaller the oscillator is compared to the wavelength of the oscillation, the more closely the oscillator approximates a point-like source. This is one reason why directional antennas have to be a certain minimum size in order to work correctly.

 

[member 529879]

http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes2.php

If you scroll down a bit on the website I linked above, there is an animation of a longitudinal wave. I don't see why a wave like this would have to propagate outwards in every direction. If you had a row of particles next to the one in the animation I would think it would remain unaffected by the moving particles in the animation.

 

[Drakkith]

http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes2.php

If you scroll down a bit on the website I linked above, there is an animation of a longitudinal wave. I don't see why a wave like this would have to propagate outwards in every direction. If you had a row of particles next to the one in the animation I would think it would remain unaffected by the moving particles in the animation.

Particles are never lined up so perfectly, so you'll always have some collisions that are off-center, transferring energy and momentum in a new direction.

 

[Nugatory]

If you scroll down a bit on the website I linked above, there is an animation of a longitudinal wave. I don't see why a wave like this would have to propagate outwards in every direction. If you had a row of particles next to the one in the animation I would think it would remain unaffected by the moving particles in the animation.

That animation is misleading for a sound wave. Typical sound wavelengths are around one meter or thereabouts, so there is an enormous number of molecules spread across each individual wave peak. Thus, the peak is not a single orderly row of molecules moving a few molecular diameters to the right and bumping into the next row - it is a entire region of higher air pressure, and of course a region of higher air pressure pushes out in all directions.

A.T. has already referred you to the Huygens-Frensnel principle; after reviewing that you might try googling for "phase array radar" to see what it takes to create a wave that really does propagate in one direction.