talking about xylophones
In: 4
For very small displacements, you can think of the metal oscillators of a xylophone as spring-like things.
The main rule about these objects is that when you apply a force, the entire object stretches or contracts proportionally to that force. That means the longer your string is, softer it is for a set amount of travel. The softness/stiffness is known as the spring constant in springs.
For these small displacements your pitch is determined entirely by the stiffness of the spring and the material’s density.
For further reading you can check out:
Springs and simple harmonic motion,
Strings as an interesting oscillator behaviour,
If you’ve got calculus and/or linear algebra background:
1-dimensional harmonic oscillator equation is a good starting point.
Stress-strain tensors is a good thing to look at too.
P.S before anyone points out: What separates these from linear oscillators is that becaue they have a shear component, the strain will not be linearly dependent on the displacement, so it isn’t really a linear oscillator except under small oscillation limit.
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