Ten - Interference
1. state and use the principle of superposition of waves:
-the ability of waves to pass through each other and temporarily occupy the same space and
combine, then carry on unaffected. the resultant wave will be found by add the
displacements (vector) of each individual wave
2. apply graphical methods to illustrate the principle of superposition:
3. explain the term coherence as two waves with a constant phase relationship over a
significant period of time
-constant phase: always the same phase difference
4. explain that coherent sources are sources that emit waves with a constant phase
relationship
5. explain interference as the addition (superposition) of two or more coherent waves,
resulting in a new wave formed
- this is the formation of points of cancellation and reinforcements
6. explain path difference as the proportion of a wavelength that two waves are "out of sync" /
one wave lags behind another
-measured in
multiples/fractions of λ
7. explain phase difference as the phase angle/proportion of a cycle by which two waves or
two different point on a wave are "out of sync"
- measured in radians,
normally multiples/fractions of
π
8. state that constructive interference is when two waves reinforce to give an increased
amplitude
- path difference is whole even number half wavelengths λ, 2λ, 3λ
-phase difference is whole wavelengths in radians 360o, 2πc
9. state that destructive interference is when two waves cancel to give a reduced amplitude
1
3
5
-path difference is whole odd number half wavelengths 2λ, 2λ, 2λ
- phase difference is half wavelengths in
radians 180o, πc
10. describe experiments that demonstrate two-source interference
- SOUND: using two loudspeakers connected to the same signal generator
-as you walk in front of the loudspeakers,
you will hear a loud sound where sound
waves have constructively interfered, and
quiet sounds where sound waves have
destructively interfered.
-we will NOT hear sounds x2 as loud as that for a single speaker
-LIGHT: involves directing a laser through a double slit
where the light falls on the screen, a series of equally spaced dots of light are seen. these bright
dots are 'interference fringes' and they are regions where light from the double slit arrive in
phase with each other i.e. constructive interference. the dark regions are destructive
interference.
-MICROWAVES: using 2.8cm wavelength microwaves which is directed towards a double gap
approx. 2.8cm in a metal barrier. the waves are diffracted at the two gaps to they spread out
to the region beyond, where they can be detected using the probe receiver. by moving the
probe around, it is possible to detect regions of high intensity and low intensity. The probe
may be connected to a meter to show the output.
11. define intensity as the rate of energy transfer per unit area at right angles to wave velocity
𝑝𝑜𝑤𝑒𝑟
𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑎𝑟𝑒𝑎
12. explain that as wave spreads out, its amplitude decreases because energy may be
absorbed/scattered
1
13. understand and use the equation 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 2
14. use the relationship 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2
- 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 ∝ √𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
- amplitudeA : 2amplitudeB
- gradient of displacementtime graph
A : 2B
-gradient shows velocity, so
velocityA : 2velocityB
1
-𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 = 2 𝑚𝑣 2
- 𝑒𝑛𝑒𝑟𝑔𝑦 ∝ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2
𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑛𝑒𝑟𝑔𝑦
,
𝑎𝑟𝑒𝑎
so intensity ∝ energy,
- overall, 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2
15. understand that when a wave is emitted from a source, the source loses energy
16. describe the Young Double-Slit experiment:
- place a monochromatic light source behind a
single slit so that the light passes through the
slit and becomes coherent
-the light diffracts until it reaches the doubleslit, and it diffracts through these gaps also
- the light from these slits are coherent, as it
starts from the same source and is in phase at
the double slit
- here it diffracts again until it reaches the
screen
- the light overlaps whilst diffracting causing an
interference pattern to occur
- on the screen, bright spots and dark spots will be visible
-Because y is an angle in both
triangles we may say
approximately
𝑎
𝜆
=
𝑥
𝐷
-rearrange to get λ =
𝑎𝑥
𝐷
a = slit separation, distance
between the centres of the slit
(found using travelling
microscopes)
x = fringe separation, distance
between the centre of
adjacent bright (or dark)
fringes
D = distance between slits to
screen
λ = wavelength
17. explain that Young's double-slit is classical conformation for the wave-nature of light
- the experiment shows that light can diffract
-shows that when two coherent light sources interfere whilst diffracting, an interference
pattern is shown by the high intensity areas (constructive interference) and low intensity
(destructive interference)
18. define monochromatic as light of one wavelength/colour/frequency