3 - Waves Flashcards
amplitude
max displacement from equilibrium position, in m
Frequency
n° of complete oscillations through a point per second, in Hz
Wavelength, λ
Length of one whole oscillation in m (distance between successive peaks)
Speed, c
Distance traveled per unit time by a wave (m/s)
c = fλ
Phase
Position of a certain point on a wave cycle (in radians, degrees or λ fractions)
Phase difference
How much a wave lags behind another, (in radians, degrees or λ fractions)
Period, T
Time taken for one full oscillation (in s’
(Frequency is 1/T)
Points in phase
both at the same point of the wave cycle, same displacement and velocity and their phase difference will be a multiple of 360° / 2π
do not need the same amplitude, only the same frequency and wavelength
Completely out of phase
odd integer of half cycles apart
e.g. 5 half cycles apart where one half cycle is 180° (π radians).
Transverse waves
oscillation of particles is perpendicular o the direction of energy
transfer
shaking a slinky vertically
e.g: electromagnetic (EM) waves (3 x 10 8 ms -1 in a vacuum)
Longitudinal waves
oscillation of particles is parallel to the direction of energy transfer
in a vacuum.
compressions and rarefactions - can’t travel in a vacuum.
e.g Sound
pushing a slinky horizontall
Polarised waves
oscillates in only one plane (e.g only up and down), only transverse waves
can be polarised
(Proof of nature of transverse)
applications: Polaroid sunglasses, TV and radio signals
Superposition of waves
displacements of two waves are combined as they pass each other
resultant displacement is the vector sum of each wave’s displacement
Constructive interference
when 2 waves have displacement in the same direction
waves have same frequency, speed, have to be in phase
Destructive interference
when one wave has positive displacement and the other
has negative displacement
equal but opposite displacements ->total destructive interference occurs
Stationary waves
superposition of 2 progressive waves same λ, f and amplitude but opposite direction
No energy is transferred
● in phase , constructive interference occurs so antinodes form (regions of maximum amplitude)
● completely out of phase , destructive interference occurs and
nodes (regions of no displacement)
Formation of stationary waves
String fixed at 2 ends, one fixed to a driving oscillator
wave from oscillator is reflected at the end of string,
First harmonic
lowest frequency at which a stationary wave forms
forms a stationary wave with two nodes and a single antinode
The distance between adjacent nodes (or antinodes) is half a wavelength (for any harmonic)
f = 1/2L • (T/μ)^1/2
μ = mass per unit length (kg/m)
T is tension
L is length of VIBRATING string
Other harmonics
Double first to get second (2 antibodies)
Triple for 3rd…
Examples of stationary waves
Stationary microwaves: reflecting a microwave beam at a metal plate, to
find the nodes and antinodes use a microwave probe.
Stationary sound waves:
The distance between each node is half a wavelength, and the frequency of the signal generator to the speaker is known so by c=fλ the speed of sound in air can be found.
Path difference
Difference in distance travelled by two waves, causes phase difference
Coherent light
same frequency and wavelength and a fixed phase difference .
Lasers are an example of light which is coherent and monochromatic
(emit single wavelength of light - form clear interference pattern)
Young double slit
Filter & single slit to make light monochromatic and coherent
light source through 2 slits (the same size as the wavelength of the
laser light so the light diffracts)
Each slit acts as a coherent point source making a pattern of light and dark fringes.
Light fringes: interferes constructively,(nλ, where n is an integer).
Dark fringes: destructive - path difference is a whole number and a half
wavelengths ((n+½)λ).
W= λD/s
w is fringe spacing
s is slit separation
D is distance between screen and slit
white light to give a wider max & less intense pttern
Lasers (core prac)
Can damage eyesight
Wear laser safety goggles
● Don’t shine the laser at reflective surfaces
● Display a warning sign
● Never shine the laser at a person
Wave nature of light proof
Young’s double slit:
diffraction and interference are wave properties, and so proved that EM radiation must act as a wave (at least some of the time).
Diffraction
spreading out of waves when they pass through or around a gap.
greatest diffraction = gap is the same size as the wavelength.
(smaller -> reflection , greater -> not as noticeable)
When a wave meets an obstacle you get diffraction round the edges, the wider the obstacle compared to the wavelength, the less diffraction
To vary width of maximum
Increasing the slit width decreases the amount of diffraction so the central maximum becomes narrower and its intensity increases .
Increasing the light wavelength increases the amount diffraction as the slit is closer in size to the light’s wavelength, therefore the central maximum becomes wider and its intensity decreases
Diffraction grating
slide containing many equally spaced slits very close together
monochromatic light is passed through a diffraction grating the interference pattern is much sharper and brighter because there are many more rays of light reinforcing the pattern.
measurements of slit widths are much more accurate as they are easier to take
dsinθ=nλ where d is distance between slits
application: line absorption soectra to detect elements in stars, cray crystallography
Refractive index (n)
property of a material which measures how much it slows down light
passing through it.
calculated by dividing the speed of light in a vacuum (c) by the speed of
light in that substance (c s)
refractive index can also be known as being more optically dense .
n of air = 1 (always > 1)
Refraction
wave enters a different medium, changes direction, either
towards (speeds up) or away from the normal depending on the material’s refractive index
n1sinθ1 (incidence) = n2sinθ2 (refraction)
Critical angle
angle of refraction is exactly 90° and the light is refracted along the boundary ,
the angle of incidence has reached the critical angle (θ c )
sin θ c = n1/n2
Total Internal Reflection
angle of incidence is greater than the critical angle and the incident refractive index (n 1 ) is greater than the refractive index of the material at the boundary (n 2 )
optical fibres
