When a stretched string is excited by a sinusoidal force, for certain frequencies its amplitude is maximum. This is referred to as resonance and occurs when the following condition is satisfied -
$$\lambda = \frac{V}{v} = \frac{2L}{n}$$Where,
\(L\) - length of the stretched string
\(n\) - an integer and can take positive values
\(\lambda\) - wavelength
\(V\) - velocity of the wave.
\(v\) - frequency of sound wave
For different frequencies, the fundamental (n=1) resonance length is found out. Standing waves are formed on the stretched string.
Velocity of Wave Propagation: The velocity of wave propagation (V) on a stretched string depends on two variables: the mass per unit length or linear density of the string (\(\mu\)) and the tension of the string (T). The relationship is given by the equation:
$$V = \sqrt{\frac{T}{\mu}}$$Where,
\(T\) - tension in the string
\(\mu\) - mass per unit length
The tension is varied using hanging weights on a lever arm. The wavelength is then measured by adjusting the frequency until a resonance pattern develops. The velocity of propagation of wave can be found using above relation.