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Q & A: are waves always sinusoidal?

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Most recent answer: 02/13/2013
Q:
What is a wave?I know this much that it is the mode of energy transfer through periodic disturbance but all what is taught is that wave is signified by sinusoidal waveform which I personally do not understand why always sinusoidal as a mode of energy transfer.Next what is the path a particle follows during energy transfer please help me get a clear picture of a wave do not hesitate in confining your answer in common language be scientific. Waiting for your reply
- Alok Singh (age 18)
Lucknow,Uttar Pradesh,India
A:
You're absolutely right that we could choose all sorts of other wave shapes for many types of waves. Ones that travel at fixed speeds, like light in a vacuum, can be written as combinations of sine waves, or of square waves, or of smooth pulses, or of little wavelets, etc. All those descriptions are equally valid, despite what some teachers say.

Things change when the speed is different for different waves, like for light in glass. Then only some special shapes of wave will propagate without changing shape. It's far simpler to use these shapes to describe the propagating light. Those special shapes, the ones that propagate without changing shape, are the sine waves. Since most waves in most media have some of this dependence of velocity on shape, we get used to using the sine waves as the basis for our description of almost all waves, even in the cases where it's not really needed.

I'm not sure what you mean by "the path of a particle.: Does this refer to what path say a water molecule takes as a wave passes it? Or are you trying to picture the wave as a set of propagating particles?

For you first question, were you looking for a more general description or just the discussion of sine waves?

Mike W.

(published on 02/12/2013)

Follow-Up #1: energy transfer by waves

Q:
I am glad you answered my query but what i meant by path of particle during energy transfer was that what actually happens that energy from sun travels down to earth through vacuum in form of waves(considering wave nature of light neglecting its particle nature), that is what happens in space time fabric which allows energy to transfer in form of waves.In nutshell what I wanted to ask is that how energy transfer takes place through waves I can't figure out that part.
- Alok Singh (age 18)
Lucknow,Uttar Pradesh,India
A:
Whoops, as often happens, I answered a different question than you intended.

Within our current theories, the spacetime fabric forms an uninteresting background for electromagnetic waves. The way the energy propagates is well described by the classical Maxwell's equations, which you can look up easily. From Maxwell's equations, one can derive that there's an energy flow proportion to ExB, where E and B are the electric and magnetic fields and "x" stands for vector cross product. (ExB is called the Poynting vector.) In a propagating wave, E and are at right angles to each other and to the wave propagation direction, so the energy just flows along in the direction the wave goes.

It's no surprise that these waves can transfer energy, since there's an energy density proportional to the square of the fields.

Please follow-up again if I'm still missing the key point.

Mike W.

(published on 02/13/2013)

Follow-up on this answer.