Topic 4 Waves Flashcards
oscillation definition
a back and forth motion about an equilibrium position
isochronous definition
an oscillation that repeats with the same time period
displacement (x) oscillations definition
instantaneous distance from the equilibrium position in a specific direction (m)
amplitude (xo) oscillations definition
maximum displacement from the equilibrium position (m)
frequency (f) oscillations definition
number of oscillations per second (Hz or s^–1)
period (T) oscillations definition
time for one oscillation (s)
phase (ø) oscillations definition
measure of how “in step” different particles are (one cycle = 360º or 2π radians)
simple harmonic motion (SHM) definition
a type of oscillation that takes place when the acceleration of (and the force on) an object is:
- proportional to its displacement from the equilibrium position
- in the opposite direction to the displacement (ie. directed towards the equilibrium position)
the motion is due to a restoring force, ie. a force that is always directed towards the equilibrium position.
acceleration against displacement graph for oscillation
- straight line shows that a∝x
- negative gradient shows a and x are in opposite directions
see pg 5 topic 4 booklet for picture
acceleration time graphs
see pg 8 topic 4 booklet for graphs
energy in shm graphs
see pg 9 topic 4 booklet for graphs
what is a wave
a movement of energy through a medium
longitudinal wave definition
the particles of the medium vibrate parallel to the direction of the energy transfer (energy prorogation) eg. sound, earthquake P waves
transverse wave definition
the particles of the medium vibrate at right angles to the direction of the energy transfer eg. light, earthquake S waves
compression
particles come together
rarefaction
particles spread out
displacement (x) wave definition
distance the medium had moved from the equilibrium position in a particular direction
unit: m
frequency (f) wave definition
number of oscillation of the medium (or complete waves passing a point) per second
unit: Hz
period (T) wave definition
time for one complete oscillation of the medium (or time for one complete wave to pass a given point)
unit: s
wavelength (λ) wave definition
shortest distance between two points that are in phase along a wave eg. crest to crest
unit: m
wave speed (c) wave definition
distance travelled per unit time by the energy of the wave (or by a wavefront)
unit: ms^–1
amplitude (A) wave definition
maximum displacement of the medium from the equilibrium position
unit: m
properties of waves
see pg 12/13 topic 3 booklet
derive the formula that shows the relationship between wave speed, wavelength and frequency
- time taken for one complete wave to pass = T
- the distance the wave has travelled in this time = λ
- wave speed (c) = distance / time = λ/T
- but T = 1/f
therefore: - c = λ/f
- => c = fλ
intensity (I) definition
“power per unit area received by an observer”
units: Wm^–2
the intensity of a wave is:
- proportional to the square of the amplitude (A) of the wave I∝A^2
- inversely proportional to the square of the distance (x) from the source I∝x^–2
mechanical wave definition
mechanical waves require a medium through which to travel
eg. sound and earthquake waves
electromagnetic wave definition
- electromagnetic waves do not require a medium so they are able to travel through a vacuum
- eg. visible light and radio waves
- all electronegative waves are transverse and travel at 3.00x10^8 ms^–1 in a vacuum
order of electromagnetic waves from low to high frequency (high to low wavelength)
Roman Men Invented Very Useful X-ray Guns
=> radio, microwave, infrared, visible, ultraviolet, x-rays, gamma
wavelengths of electromagnetic waves
radio: 10^2 m
microwave: 10^–3 m
infrared: 10^–5 m
visible: 10^–7 m
ultraviolet: 10^–9 m
x-ray: 10^–12 m
gamma: 10^–14 m
what two things happen at the boundary when waves travel from one medium into another
- some of the wave’s energy will be reflected
- some of the wave’s energy will enter the medium but will change speed - this change in speed is called refraction
name all the rays, angles etc. in a medium graph
incident ray
normal
reflected ray
refracted ray
angle of incidence (i)
angle of reflection (r)
medium 1/2
angle of refraction (r)
what happens when a waves goes from a faster medium to a slower one
bends towards the normal
what happens when a waves goes from a slower medium to a faster one
bends away from the normal
what happens when a waves enters a different medium at 90º
not change direction
snell’s law
n = sin i ÷ sin r
can only be used if the first medium is AIR
total internal reflection occurs when:
- light is travelling from a more to a less optically dense medium (ie. it is speeding up/n is getting smaller)
- the angle of incidence at the boundary is greater than the critical angle (θc)
sin θc =
1/n1
(only is light is travelling from the medium INTO AIR)
what is a wavefront
a line connecting points on a wave with the same phase/displacement
eg.
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what is a ray
- a line drawn to represent the direction a wave is travelling when viewed from above
- rays are drawn at 90º to the wavefront
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how to draw reflected wavefronts
- draw the normal
- draw the reflected ray
- draw the wavefronts at 90º to the reflected ray
how to draw refracted wavefronts
- draw the normal
- draw the refracted ray
- draw the wavefronts at 90ºto the refracted ray
what is diffraction
- when waves move past an obstacle or through a gap the waves tend to spread out
- longer wavelengths diffract more
- if gap width = wavelength, circular wavefronts are produced
- amplitude will decrease as the energy is spread out over a longer wavefront
what is constructive interference
if the waves meet in phase they will form a resultant wave with an amplitude equal to the sum of the two individual waves
the superposition is twice the height
what is destructive interference
if the waves meet out of phase they will cancel each other our to give a wave of zero amplitude (assuming both waves are of equal amplitude)
the superposition is canceled out
principle of superposition
“if two or more waves meet, the resultant displacement at any point is found by adding the displacements produced by each individual wave”
circular wave interference pattern
2 antinodal
1 nodal
1 antinodal
0 nodal
0 antinodal
0 nodal
1 antinodal
1 nodal
2 antinodal
antinodal lines
- waves meet in phase
- constructive interference
- path difference = nλ
- maximum amplitude “maxima”
nodal lines
- waves meet out of phase
- destructive interference
- path difference = (n+1/2)λ
- zero amplitude “minima”
light antinodal line and nodal line brightness level
antinodal: bright
nodal: dark
sound antinodal line and nodal line loudness level
antinodal: loud
nodal: quiet
double slit interference - young’s experiment
- ‘light source’ shining through a ‘double slit’ where the distance between the slits is ‘d’
- ‘diffraction’ occurs when the light passes through the slit
- the light ‘interferes’ with each other and creates an ‘interference pattern’
- dark and bright ‘fringes’ are seen
- s = λD/d
where:
- s is the distance between the bright fringes
- λ is wavelength of the light
- d is the distance between the double slits
- D is the distance from the double slits to interference pattern on a screen
and all distances are in meters
standing waves form when:
- two waves of the same type meet and they must be:
- of the same amplitude
- of the same frequency
- travelling in opposite directions
they only form if the λ fits the string
fundamental frequency definition
lowest f at which a standing wave forms
how is a wave reflected at the open end
- as the air moves outwards it creates a low pressure region behind it that pulls the air back into the pipe
strings and pipes have a ______ of _______ ___________ (_________) at which they will form standing waves
strings and pipes have a range of resonant frequencies (harmonics) at which they will form standing waves
strings and open pipes can produce ____ ___________
strings and open pipes can produce all harmonics
closed pipes can only produce ____________ ___________
closed pipes can only produce odd-numbered harmonics
amplitude of standing waves
all points along the wave have different amplitudes. maximum amplitude at the antinodes, zero at the nodes
amplitude of travelling waves
all points along the wave have the same amplitude
wavelength of standing waves
λ is twice the distance from one node (or antinode) to the next node (or antinode)
wavelength of travelling waves
λ is the shortest distance between two points that are in phase
phase of standing waves
all points along the wave are moving in phase or 180º out of phase (except for the nodes which do not move)
phase of travelling waves
all points along the wave have different phases
energy of standing waves
energy is not transmitted by the wave but it doe posses energy
energy of travelling waves
energy is transmitted by the wave
frequency of standing waves
all points along the wave oscillate at the same frequency
frequency of travelling waves
all points along the wave oscillate at the same frequency
polarisation
- the oscillation of the medium is only in one plane
- only transverse waves can be polarised
electromagnetic waves are made up of:
- oscillating electric and magnetic fields that are perpendicular to each other
definition of polarisation
the electric field vector is oscillating in one plane only
Brewster’s Law
- reflection off a surface
- it will be polarised in the place of the surface
- eg. if it reflects of a horizontal surface it will be polarised horizontally
see pg 33 topic 4 booklet for diagram
for polarised light, n=
n = tan ø
Malus’ Law:
polarising filter
a polarising filter polarises light
(it is made up of chain crystals embedded in a transparent film. the polaroid restricts the electric field vector of electromagnetic waves passing through it to a direction perpendicular to the chains)
Malus’ Law:
analyser
a device that can detect polarised light
(analysers allow through components of polarised light in a preferred direction. If the angle between the polarisation of the incident light and the preferred direction is 0º to 90º then some light will pass through. if the angle = 90º then no light passes through)
Malus’ Law
I = Io(cos θ)^2
I = intensity of transmitted light (W m^–2)
Io = intensity of incident light (W m^–2)
θ = angle between plane of polarisation of incident light and the analyser’s preferred direction
if UNPOLARISED light passes through a polariser, the…
light intensity will be reduced by half
interference pattern occurs when
two waves must have the same plane of polarisation in order to produce an interference pattern
do waves of different planes of polarisation cancel or add or other
waves of different planes of polarisation cannot cancel out or add together - they create a wave of a different plane of polarisation
optically active substances
- sugar solutions
- stress analysis
- LCDs (liquid crystal displays)
see pg 35 topic 4 booklet for how they work
optically active substances
- sugar solutions
- stress analysis
- LCDs (liquid crystal displays)
see pg 35 topic 4 booklet for how they work
