Resonant frequencies of stretched string with fixed ends¶

For a string with fixed ends there is only a limited set of frequencies at which standing waves will occur on it. Each possible frequency is a resonant frequency, and the corresponding wave pattern is an oscillation mode. The oscillation mode corresponding to \(N = 1\) is called the fundamental mode or the first harmonic, the mode corresponding to \(N = 2\) is the second harmonic, and so on.

Links:

Wikipedia.

resonant_frequency¶: Resonant frequency of the \(m\)-th harmonic. See temporal_frequency.

Symbol:: f
Latex:: \(f\)
Dimension:: frequency

harmonic_number¶: An integer called harmonic number. See positive_number.

Symbol:: N
Latex:: \(N\)
Dimension:: dimensionless

phase_velocity¶: phase_speed of the wave.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

string_length¶: length of the string.

Symbol:: l
Latex:: \(l\)
Dimension:: length

law¶

f = N * v / (2 * l)

Latex:: \[f = \frac{N v}{2 l}\]