6
votes
5answers
241 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 ...
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 ...
2
votes
1answer
235 views

How can Hilbert spaces be used to study the harmonics of vibrating strings?

The overtones of a vibrating string. These are eigenfunctions of an associated Sturm–Liouville problem. The eigenvalues 1,1/2,1/3,… form the (musical) harmonic series. How can Hilbert spaces be ...
-1
votes
1answer
619 views

resonance frequency [closed]

A string has a mass per unit length of 9 10–3 kg/m. What must be the tension in the string if its second harmonic has the same frequency as the second resonance mode of a 2m long pipe open at one end? ...