For waves on musical strings (such as in a piano) the wave
speed is not exactly constant, but increases a small amount
with increasing pitch. Hence, the overtones for a piano
string are actually a little bit sharp. This is why the
lowest notes on a piano are usually tuned a little flat (so
their overtones are "in tune" with the higher notes) and
the highest notes are tuned a little sharp (so they are
"in tune" with the overtones of lower notes).
A change in wave speed with frequency is known as "dispersion."
For light waves, dispersion (for the light travelling through water)
is what gives us rainbows.
Note that the "wave speed" for vibrations of the string and
the "sound velocity" for sound wave travelling through air
(approx 1100 ft/sec) are very different.
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Back to Overtones
to Physics of Music Notes