Physic of Zimbabwean Marimba

    As a small note before getting into the physics of marimba, let me briefly
mention the properties of a standing wave. Standing waves are emitted when
instruments are played, emitting a wave the oscillates back and forth, creating
both nodes and anti-nodes. As can be seen in the picture below, nodes are the
point where the wave remains motionless, while anti-nodes are where the wave
oscillates back and forth between its maximum positive and negative amplitudes.

http://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/stand.gif
http://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/stand.gif

The actual physics behind marimba isn't all that difficult at all. When a bar is a struck,
the sound wave travels down the resonator, causing it to vibrate. Since the resonator is
open on both ends, each end as well as the middle point is considered an anti-node. The
equation used to calculate the frequency of the note is expressed as:


Where:

v is the speed of sound in the material of the bar
L is the length of the bar
M is 3 at n =1, 5 at n=2, 7 at n=3, etc. (2n+1)
K is as below: