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Stationary waves, diffraction and interference

Stationary waves, diffraction and interference

Principle of superposition

The Principle of Superposition states that when two or more waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves at that point.

principle of superposition

For constructive interfernce: the resultant displacement is always higher than the displacement of the individual waves.

For destructive interfernce:the resultant displacement is always smaller than the displacement of the individual waves.

Stationary waves

A stationary wave is formed by two progressive waves of the same type, amplitude and frequency travelling in opposite directions superpose.

show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns

Microwaves

microwave

The Microwave source generate the wave signal while the metal reflector reflect the wave back, by this there the two progressive waves will superpose.

Stretched string

stretched string

explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes

nodes and antinodes

For the first waveform: it is the first harmonic or the fundamental

first harmonic

for the second waveform: it is the second harmonic or the first overtone

second harmonic

for the third waveform: it is the third harmonic or the second overtone

third harmonic

Pipes closed at one end and pipes open at both ends

open and closed pipe

pipes on the left hand side are open at one end

For the first harmonic

capture

pipes on the right hand side are open at both end

For the first harmonic

capture

Node: it is a point of zero amplitude

Antinode: it is a point of maximum amplitude

Recall,

formula for wave velocity

Differences between stationary and progressive waves

staionary waves

  1. No energy is transported by the wave
  2. the wave profile does not advance
  3. amplitude varies from maximum at the anti-nodes to zero at the node

Progressive waves

  1. energy is transported in the direction of the wave
  2. wave profile advances
  3. amplitude is the same for all particles in the wave

Diffraction

Diffraction is the spreading of waves through an aperture or round an obstacle.

  • The bending of waves around an obstruction
  • As the size of the aperture or the object decreases the effects of diffraction increase
  • The wavelength needs to be similar to the size of the aperture for diffraction to be noticeable

The smaller the size of the aperture, the greater the spreading of the waves (if the width of the aperture is about the same size as the wavelength, λ, the diffraction effect is very considerable).

diffraction grating

Diffraction grating

A diffraction grating is a plate on which there is a very large number of identical, parallel, very closely spaced slits.

Uses of diffraction grating

  1. it is use to determine the wavelength of light
  2. it can be used to make spectrometer

spectrometer

spectra range

Diffraction grating equation can be represented by

diffraction grating equation

n is the number of order

λ is the wavelength

d is the slit sepation

ø is the angle of diffraction

Interference

Interference is the superposing of two or more waves to give a resultant wave whose displacement is given by the principle of superposition.

superposition_maxima_minima

At regions of maxima, constructive interference occurs (i.e the waves arrive at these points in phase), resulting in maxima amplitude, hence high intensity

At regions of minima, destructive interference occurs (i.e the waves arrive at these points in anti-phase), resulting in minima or zero amplitude, hence low or zero intensity.

Young’s double slit experiment

young's double slit

Monochromatic light talks about light with one wavelength, example red light

polychromatic light consists more than one wavelength, example visible or white light

Coherent source: waves coming from them are always at a constant phase difference

Bright fringes are formed due to constructive interference(i.e the waves arrive at these point in phase), while

Dark fringes are due to destructive (i.e the waves arrive at these points is anti-phase(180 degree)- no resultant amplitude, which then appear dark)

For interference fringes to be observable

  1. The source must be coherent; that is they must maintain a constant phase difference
  2. The source must have the same frequency (for light waves, this mean that they must be monochromatic)
  3. The pronciple of superposition must apply(the source must produce the same type of waves)
  4. The source must have approximately the same amplitude

Condition for constructive interference

constructive interference

condition_constructive_interference

B is the second source

A is the first source

Condition for destructive interference

formula_destructive_interference

interference equation

λ is the wavelength

a is the separation of the slits

x is the fringe separation

D is the separation between the screen and the double slit

 

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