Friday, 18 May 2007

Friday's Physical Law - Mexican Wave

Last time we mentioned that one simple harmonic oscillator (SHO) couple to another SHO can have interesting effects. In fact when you have one SHO coupled to another SHO coupled to another SHO... you get a oscillation that varies not only in time but also in space and what we have is a wave.

Yes you can think of it just like the Mexican wave at you favourite sporting event (ok now that is an interesting thought - can anyone tell me where that name comes from?) first one person stands up and then the next and so on. The main difference between coupled SHO and drunk sports fans is that with sports fans you get a single pulse travelling around the ground (or very occasionally two pulses), but with the coupled SHOs each one continues to oscillate so you get a series of pulses following (often quite rapidly) one after the other.

So what exactly is meant when I say the oscillations varies in time and space. We know from last time how the SHOs vary with time, and that is carried through to the behavior of waves. We see each individual point oscillating with the same equations for position and velocity and acceleration. The variation in space can be described in a very similar way, as a cos or sin function varying with respect to position rather than time. Obviously the angular frequency term of the time variation is also replaced by a term that is related to how the wave repeats in distance, this is sometimes know as the wave vector (k). Remember:

  • ω = 2π/T
well similarly

  • k = 2π/λ
where λ is the wavelength of the wave and is the distance over which the oscillation repeats, much like T is time in which the oscillation repeats.

But what exactly are the oscillators that we are talking about, well these can be almost anything, ok not anything but waves happen in lots of different materials. The obvious examples of waves is those on water, but almost all musical instruments make sounds with waves and then there are earthquakes and electromagnetic radiation and ...

Stay tuned for more exciting developments next time