Adding Simple Harmonic Waves I demonstrates the superposition of
two simple harmonic waves.
You can change the amplitudes: A,
and angular frequencies: w = 2*pi*f of two waves which will be combined
to form a third wave.
A short theoretical background on this phenomena is available in
dvi,
postscript or
pdf formats.
Things to do
Interference
Investigate the interference of two waves with the same frequency w1= w2, and
different phase constants phi.
Try w1 = w2 = 0.1,
phi1 = 0, and vary phi2 between -pi and pi.
Beats
Combining waves with two waves with similar but not identical frequencies leads to the phenomena of
"beats". For example two musical notes with angular frequencies w1, and w2,
lead to a note whose pitch has an angular frequency:
wave = (w1 + w2)/2
where the amplitude of this sound waxes and wanes with an angular frequency:
wmodulation = (w1 - w2)/2
Note that since the absolute value of the amplitude waxes and wanes twice
during each modulation cycle, a beat is heard with an angular frequency wbeat = (w1 - w2)
