Piano 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:
A piano string is pq.m long and has a mass of pq.g. abcliste abc How much tension must the string be under if it is to vibrate at a fundamental frequency of pqHz? abc What are the frequencies of the first four harmonics? abcliste
Solution:
abcliste abc The wavelength of the fundamental is lambda_ l pq.m. The speed of a wave on this string is therefore c lambda f pq.m pqHz pq. The tension in the string has to match F fracmlv^ pqN. abc The consecutive frequencies are pqHz pqHz and pqHz. abcliste
A piano string is pq.m long and has a mass of pq.g. abcliste abc How much tension must the string be under if it is to vibrate at a fundamental frequency of pqHz? abc What are the frequencies of the first four harmonics? abcliste
Solution:
abcliste abc The wavelength of the fundamental is lambda_ l pq.m. The speed of a wave on this string is therefore c lambda f pq.m pqHz pq. The tension in the string has to match F fracmlv^ pqN. abc The consecutive frequencies are pqHz pqHz and pqHz. abcliste