Guitar string
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The following quantities appear in the problem:
Länge \(\ell\) / Masse \(m\) / Kraft \(F\) / Geschwindigkeit \(v\) / Frequenz \(f\) / Wellenlänge \(\lambda\) / Massenbelegung \(\mu\) /
The following formulas must be used to solve the exercise:
\(m = \mu \cdot \ell \quad \) \(\lambda = \frac{\ell}{2} \cdot n \quad \) \(c = \lambda \cdot f \quad \) \(c = \sqrt{\frac{F}{\mu}} \quad \)
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Exercise:
The length of a guitar string is lO and its mass is mO. The distance from the bridge to the support post is dlO and the string is under a tension of FO. What ist the frequencies of the fundamental tone?
Solution:
The string has mu fracmL fracml mb mass per meter length of string. Under FO tension waves propagate on the string with c sqrtfracFmu sqrtfracFmb c velocity. The wavelength of the fundamental is lambda ell dl lam so the frequency is f fracclambda fracclam f.
The length of a guitar string is lO and its mass is mO. The distance from the bridge to the support post is dlO and the string is under a tension of FO. What ist the frequencies of the fundamental tone?
Solution:
The string has mu fracmL fracml mb mass per meter length of string. Under FO tension waves propagate on the string with c sqrtfracFmu sqrtfracFmb c velocity. The wavelength of the fundamental is lambda ell dl lam so the frequency is f fracclambda fracclam f.