4.4.3: Superpostion

Question 1

Superposition

Answer 1

When two or more progressive waves meet and overlap, they superpose, producing a single wave. When tow waves meet at a point, the resultant displacement of the wave is equal to the sum of displacements of the individual waves.

Question 2

Constructive Interference

Answer 2

The individual displacements are in the same direction and add up

Question 3

Destructive Interference

Answer 3

The displacements are in opposite directions and counteract/ cancel each other out

Question 4

Coherence

Answer 4

Two waves are coherent when they are emitted with a constant and unchanging phase difference (eg π radians).

Question 5

Interference

Answer 5

The superposition occurring between two coherent waves. When two coherent waves interfere, the maximum resultant displacement occurs when phase difference is an even multiple of π, so the two crests of the wave combine. The minimum resultant displacement occurs when the phase difference is an odd multiple of π, so one crest and one trough act to cancel each other out.

Question 6

Path Difference

Answer 6

The difference in distance that the two waves must travel from their sources to a particular point. If the path difference is a multiple of π, there is constructive interference. If it is a multiple of π/2, there is destructive interference

Question 7

Two source interference with sound

Answer 7

Two audio signal generators can be set up side by side. They will both emit coherent waves in all directions which will overlap to form an interference pattern. This means there will be areas of loud noise and areas of quiet due to constructive and destructive interference.

Question 8

Young’s double slit experiment to determine λ of light and investigate superposition

Answer 8

A laser which produces monochromatic light is place behind a sheet with two small slits in it, a distance ‘a’ apart. The two coherent waves produced by the diffraction through the slits overlap and superpose, creating alternate bright (maxima) and dark (minima) fringes on a screen ‘D’ away from the slits. The distance between adjacent maxima is ‘x’. The equation
λ= ax/d
can be used to determine wavelength of light.
a««<D

Question 9

Determining λ of light using diffraction grating

Answer 9

The light passes through the diffraction grating and produces an interference pattern with bright and dark maxima and minima. The number of slits is usually given per cm and must be converted to the value ‘d’, the distance, in metres between each slit. ‘n’ is the order of maxima and θ is the angle between the 0th and nth maxima. The formula
d sinθ = nλ
can be used