-1
votes
1answer
35 views

String vibration

In many textbooks an illustration of a vibrating string at a fundamental mode shown (and wikipedia) shown like this http://en.wikipedia.org/wiki/File:Standing_waves_on_a_string.gif). However if you ...
6
votes
5answers
211 views

Why do harmonics occur when you pluck a string?

When you energise a taut string, the following resonant modes of vibration occur: Plotting on the frequency domain, you can see their corresponding frequencies: But what is the underlying ...
1
vote
1answer
199 views

How do I recover the 1D wave equation from the Lagrangian?

Consider small displacements, $y(x,t)$, of an element of a string (circled in red and shown below) from equilibrium. The force balance in the vertical direction yields: $$+\uparrow \Sigma F: ...
0
votes
2answers
2k views

Young's Modulus and Vibrating String Harmonics

I was wondering how Young's Modulus effects the resonant harmonics of a vibrating (string instrument) string. I know that the string's fundamental frequency is $$\frac{1}2 \times \text{Length} \times ...