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
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:
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