[sdiy] Generating acyclic waveforms?

[Ian Fritz]

At 03:19 PM 3/21/2010, Tom Wiltshire wrote:
>Does anyone (physicists?) on the list know whether this harmonic
>stretching occurs only with strings, or do similar things happen in
>wind instruments? reeds?
>
>What I'm really asking is whether this is a 'string' effect or an
>'acoustic' effect.

It's a string effect.  The higher harmonics require a sharper bending 
radius and therefore they see a stiffer elastic constant.  Since the string 
is vibrating freely, the higher frequencies run back and forth faster than 
the lower ones.

You wouldn't see a significant effect like this in winds because the waves 
are longitudinal waves in air and therefore have negligible 
dispersion.  Additionally, driven systems such as winds excite coherent 
waves, so there can be no speeding up of specific harmonics over many cycles.

Other percussive instruments such as stricken bars are just an extreme 
extension of the string phenomenon, although more complicated because of 
the qualitatively different kinds of modes that can be excited.

   Ian