Chapter 6 - Waves
Superposition and Coherence:
Superposition occurs when 2 or more waves pass through each other.
At the instant the wars cross, the displacements due to each wave combine. Each wave then continues on in the original direction.
Principle of superposition = when 2+ waves cross, the resultant displacement is the vector sum of the individual displacements.
Interference can be constructive or destructive.
A crest + A crest = a bigger crest & a trough + a trough = a bigger trough. ∴ constructive.
A crest + a trough (of equal size) = 0. The 2 displacements cancel each other out completely ∴ destructive.
If crest /trough aren't the same size the inference isn't total. For interference to be noticeable the amplitudes should be almost equal.
You can use phasors to show superposition
You can use little rotating arrows to represent the phase of each point on a wave.
The phasor rotates ANTICLOCKWISE through one whole turn as the wave completes a full cycle.
To find resultant at timer, add the phasors tip to tail.
In PHASE means In STEP, 2 points in PHASE interfere CONSTRUCTIVELY.
2 points on a wave are in phase if they are both at the same point in a wave cycle.
Often use one wave cycle as 360 degrees (2π radians).
Points that have a phase difference of 0 or a multiple of 360 degrees are in phase ∴ phasors are pointing in same direction.
Points with a phase difference of odd-number multiples of 180 degrees are exactly out of phase. This is called ANTI PHASE. Their phasors point in opposite directions.
Points can have a phase difference of any angle.
You can talk about 2 different waves being in phase. In practice this happens because both waves came from the same oscillator.
In other situations, nearly always be a phase difference between 2 waves.
To get interference patterns the 2 sources must be coherent.
Interference happens in a jumble when observing waves of different wavelength and frequency.
To get clear interference patterns the 2+ sources must be coherent.
2 sources are coherent if they have the same wavelength and frequency and a fixed phase difference between them.
Constructive/Destructive Interference depends on path difference.
Constructive/Destructive depends on how much further one wave has travelled that the other wave.
The amount by with one waves path is longer is called the path difference.
Constructive interference occurs when path difference = number x wavelength
Destructive Interference occurs when path difference = (number+1/2) x wavelength
You get standing waves when a progressive wave is reflected at a boundary
A standing wave is the superposition of 2 progressive waves with the same wavelength, moving in opposite directions.
Unlike progressive waves, standing waves transmit no energy.
You can demonstrate standing waves by setting up driving oscillator at the end of a stretched string with the other end fixed. Wave generated is reflected back and forth.
For most frequencies the resultant pattern = jumble. If…