Dispersion

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.

There are no pop-ups or ads of any kind on these pages. If you are seeing them, they are being added by a third party without the consent of the author.