# Waves

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. After you have entered a new value, click on “Blue” or “Green” to see the effect. You can also hide the blue and green waves to show the result of adding them a bit more clearly.

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.