|
When two waves of equal wavelength, amplitude and frequency moving in opposite directions in a stationary medium interfere, the resulting wave is called a standing wave. In this case no net propagation of energy takes place.
Let us consider two waves of equal wavelength, amplitude and frequency traveling in opposite directions such that they are represented as:
 and 
Here, y0 is the amplitude of the wave, ω is the angular frequency, k is the wave number, x is the position along x-axis and t is the time. Now the resulting standing wave will have displacement,
At nodes x has values equal to 0, λ/2, λ, 3λ/2,……….etc. And at antinodes x has values equal to λ/4, 3λ/4, 5λ/4,…………….etc. Note that the nodes are the points of destructive interference and the antinodes are the points of constructive interference.
Standing Waves and Resonance:
When two waves having same wave length, amplitude and frequency traveling in opposite direction superpose each other then a standing wave is formed. If the frequency of the new wave after interference is equal to the natural frequency of the individual wave then the condition is called resonance.
If a periodic force is applied to such a system which is capable of oscillating in one or more normal modes then the amplitude of the resulting motion is greater than normal when the frequency of oscillation of the applied force is equal to the natural frequency of the system. This phenomenon is called resonance.
|
Waves and Optics