P12

Question 1

Superposition of waves

Answer 1

when two waves pass through each other they produce a single wave
where instantaneous displacement is found by summing each waves displacement
Needs to be same frequency - so constant phase difference and coherent - but not necessarily same amplitude

Question 2

Interference

Answer 2

when two waves are in phase then max +ive displacements line up so resultant has even more amplitude - constructive interference - as intensity proportional to amplitude^2 intensity increases so e.g sound is louder
if two in antiphase then max +ive lines with max -ive and displacement smaller - destructive interference - if waves have same amplitude then resultant has 0 amplitude - cancelled out completely

Question 3

Path difference

Answer 3

The difference in distance travelled by two waves from their source (measured in λ wavelength)

Question 4

path/phase difference and interference

Answer 4

central maxima, as you move one up/down you get first/second and so on minima then maxima
at minima path difference is odd number of half wavelengths (0.5, 1.5….)
at maxima path difference is whole number (1, 2)
path difference of 1λ = phase difference 2π

Question 5

Youngs double slit

Answer 5

Monochromatic source of light by using a filter (to ensure constant frequency, phase difference, coherence), diffracted by a single slit, then diffracted by a double slit where each slit is a different source of coherent waves
Interference pattern seen on screen with stripes of bright and dark fringes

Question 6

Young’s double slit equation

Answer 6

λ = ax/D
where a is separation between slips, x is separation between bright fringes (ideally measure this from fringe edges), and D is distance from slits to screen
D must > a or proper interference pattern wont appear

Question 7

stationary waves

Answer 7

two progressive waves with same frequency (ideally also amplitude) in opposite directions superpose - some points in antiphase and cancel out - node, some points in phase so greatest amplitude - antinode
distance between adjacent nodes = λ/2
drawn like a double helix strand

Question 8

Phase difference in stationary waves

Answer 8

In between adjacent nodes -All in phase as all reach max displacement as same time, but amplitude differs
On different sides of a node - antiphase as one side reaches max positive as other side reaches max negative

Question 9

Stationary vs progressive waves

Answer 9

Progressive has no net energy transfer as opposite direction waves, twice the difference between notes = λ
Progressive only has phase change across one complete cycle, and all parts have same amplitude

Question 10

String stationary waves

Answer 10

Stretched between fixed points - they act as nodes - plucked so progressive waves travels and reflects off end - creates opposite 2 progressives which form a stationary

Question 11

First Harmonic

Answer 11

First harmonic is fundamental mode of vibration i.e what will get when a string is plucked normally - fundamental frequency based on mass, tension, length

Question 12

Harmonic patterns

Answer 12

Each pattern must have a frequency integer multiple of F0 (fundamental)
At fundamental the stationary is half a wave so wavelength = 2L (L is length of string)
At each integer up you add half a wavelength - or add a node + antinode

Question 13

Stationary waves in air columns

Answer 13

Closed at one end - air cannot moved at closed end so acts as a node, air moves most at open end so antinode - only these two at fundamental frequency so 1/4 of a wavelength then every other integer multiple adds 1/2 λ (1/4 doesnt work so not all frequency multiples possible)
2 open ends - air moves most so 2 antinodes and node at centre - all frequency multiples work adding 1/2 λ each