Wavelength of standing wave in string with fixed ends

If a standing wave occurs in a string with fixed ends, the value of the displacement function \(q(x)\) must be zero on both ends of the string. To satisfy this boundary condition, only an integer number of half-waves can fit into the total length of the string.

Conditions:

1. Boundary condition: \(q(0) = q(L) = 0\).

Links:

1. Wikipedia.

integer_factor

Positive integer, also called harmonic number of the \(n\)-th harmonic. See positive_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

wavelength

wavelength of standing wave.

Symbol:

lambda

Latex:

\(\lambda\)

Dimension:

length

string_length

length of the string.

Symbol:

l

Latex:

\(l\)

Dimension:

length

law

N * lambda / 2 = l

Latex:

\[\frac{N \lambda}{2} = l\]