The reflected wave can be described by the equation,
$$y_{2} = y_{m}sin\left( \frac{2\pi}{\lambda}(x + vt)\right)$$Resultant standing wave can be described by,
$$y = 2y_{m}sin\left( \frac{2\pi}{\lambda}x\right)cos\left( \frac{2\pi}{\lambda}vt\right)$$Resonance: At certain frequencies of oscillation all the reflected waves are in phase, resulting in a very high amplitude standing wave. These frequencies are called resonant frequencies. In general, resonance occurs when the wavelength satisfies the condition:
\(\lambda= 2L /n\); \(n\) = 1, 2, 3, 4…
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:
$$V = \sqrt{\frac{T}{\mu}}$$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 can then be calculated using the relationship \(V = \lambda v\) and the effects of tension and linear density on velocity can be determined.