This animation shows you the result
of adding two sine waves together. This is what happens in an AM radio
transmitter when the radio carrier wave is modulated by an audio wave. The
audio wave has frequencies between 30 Hz and 20 KHz depending on the
source of the sound. The carrier wave depends on the band being used to
transmit the wave. It could be as low as 1.8MHz for a short wave
transmitter or as high as 460 MHz for VHF radio. Even higher frequencies
are possible for microwave transmitters. Here the frequencies are measured
in GHz.
In the last frame of the animation,
you can add your own values for the blue and green waves. Experiment with
different values to see some interesting results. For instance entering 3
and 20 or 3 and 21 produces a surprising difference.
If you enter a value of 80 you will
see a single sine wave. In contrast, entering 4 will produce about 25
waves.
The formula for a sine wave is:
y = sin
x
The formula for adding two waves is:
y
= ½ sin x + ½
sin z
You should be able to
see that where both waves peak, the resultant wave also has a peak. Where
one wave peaks, but the other has a trough, the two cancel each other out.
Other
interesting waves are produced where the two waves to be added have the
same frequency, but are out of phase. This is something for you to think
about. You could try using the equations which I have given you to produce
your own sine waves. Try it with your spreadsheet.
