Superposition occurs when 2 waves travelling in the same medium meet
Their amplitudes combine algebraically to produce a resultant wave at that particular instant
When the 2 waves superimpose, the resultant displacement of the particles is equal to the algebraic sum of the individual displacements of the original waves
Constructive Interference
2 waves of equal frequency that are in phase interfere/superimpose
Resultant wave has an amplitude greater than each of the individual waves
Equal to the sum of the amplitudes of the individual waves
Application: Amplified Speakers
When 2 speakers are made to produce the same sound, the sound waves produced interfere with each other
Thus, at certain places (anti-nodes), constructive interference occurs, and the sound is louder (amplitude increases)
At nodes, destructive interference occurs, and the sound is quieter (amplitude decreases)
Destructive Interference
2 waves of equal frequency that are not in phase meet and superimpose, crating a resultant wave that has amplitude lower than each of the individual waves
Here the individual waves have positive and negative amplitudes, and so they combine to produce a wave of smaller amplitude
Complete Destructive Interference
2 waves of equal frequency that are completely not in phase, i.e. 180˚ out of phase, combine
Negative amplitude of one wave, and the positive amplitude of other combine to completely cancel out at the instant when they meet
Application: Noise Cancelling Headphones
Incoming sound waves have specific waveforms
External microphones detect this ambient sound and invert the waveform
As the ambient sound and inverted sound are 180˚ out of phase, complete destructive interference occurs, and thus the listener hears nothing
The inverted sound is such that it does not combine with the music sound wave, thus listeners can still hear their music
Standing Waves
Resultant wave that forms when 2 waves of equal frequency and amplitude that are moving in the opposite direction meet
No net transfer of energy
Wave does not travel in any direction
Nodes: In a standing wave, there are moments when the 2 identical waves travelling in opposite directions are 180˚ out of phase; here a complete destructive interference occurs, and there is no particle displacement
Anti-nodes: There are also moments when 2 identical waves are in phase and so complete constructive interference occurs and there is maximum particle displacement; here the particles vibrate about the equilibrium position but do not propagate in any direction