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:

1. 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:

$$f=\frac{Nv}{2l}$$