Detector Watch 2

Well, it's Sunday evening again. I'm sick of studying for maths and IT exams - what I've been doing all week - so I'll take some time off, and look at harmonics.

Let's recall our good friend the sine wave:

Here the signal rose and fell between some extremes - the amplitude. It did so in a certain time - the period - which ( when measured in seconds ) if you took the reciprocal, you got the frequency.

Let's look at what happens if we change the frequency only - by some exact/integral multiples:

Now with another friend, the Fourier Transform, we can describe this behaviour thus:

As a general rule for pretty well any wave-like phenomenon, the energy in a given waveform increases with frequency. For light that is certainly true ( with E = Energy, h = Planck's constant, and v = frequency. * means multiply ):

E = h * v

Many resonant systems/behaviours tend to distribute energy in a number of multiples of a given frequency, but because the higher frequencies 'cost' more energy then each of those is less 'affordable'. Also the higher frequencies usually decay and subside quicker, with the energy being dealt into some other form. Check this out, from Livingstone:

which indicates energy at peaks of 60Hz, 120Hz, 180Hz, 240Hz and 300Hz. This is the fundamental and harmonics of the alternating current power supply frequency in the US.

Try these ones, from Hanford:

which demonstrate a so called 'violin mode' of oscillation, and many harmonics. Note how the same 'structure' of the lowest frequency pattern is preserved. Also see how the amplitude, with each increase in frequency, steadily goes down and in this plot ( for the ninth harmonic ) is hardly above the forest of noise:

Of course, a really good question is why do such multiples exist? But that'll be another day.... :-)

Cheers, Mike.