Waves Flashcards
Amplitude
The magnitude of the maximum displacement reached by the oscillation in the wave.
Wavelength
The distance between one point on a wave and the same point on the next cycle of the wave.
Frequency
The number of complete wave cycles that pass a point per second.
Period
The time taken for one complete oscillation at one point on a wave.
Wave types:
- Transverse waves
- Longitudinal waves
Transverse waves
The vibration/oscillation of
the wave is perpendicular to the direction of the wave.
Longitudinal Waves
The vibration/oscillation of
the wave is parallel to the direction of the wave.
Longitudinal waves:
- Sound, ultrasound, infrasound…
- Human hearing range is 20Hz - 20kHz
- Infrasound describes waves with a lower limit of human audibility (generally 20Hz)
- Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing
Progresive waves
Waves which move and transmit energy
Longitudinal waves show:
- Areas of high pressure called compressions
- Areas of low pressure called rerefactions
Equilibrium
A restoring force that brings the particles back toward their equilibrium position
Transverse waves:
- Electromagnetic waves
- Vibrations on a guitar string
- Waves on a rope
- Seismic S-waves
Wavefront (simple)
Lines which represent the same point on a wave (e.g. crest)
Phase difference
The difference in phase between two points on a wave.
Two points on a wave are in phase…
when they are the same point in their wave cycle
Superposition:
- When two waves meet
- The displacement of the resultant wave is equal to the sum on the individual displacements of the two waves
- Afterwards, each wave will continue past each other, as the energy progresses in the same direction it was originally travelling.
Superposition of continues waves:
- When the two waves are in-phase, they interfere constructively.
- When the two waves have opposite-phase, they
interfere destructively and
cancel each other out.
Coherence
Waves are coherent if they have the same frequency and constant phase difference
Explain how noise cancelling headphones work
- Use the principle of superposition of waves
- Sound waves detected by a microphone
- Electronic signal sent to loud speaker to produce an inverted wave
- Two waves must be 180º out of phase
- Causing cancellation/ destructive interference
Interference
When two coherent sources of continuous waves interact, an
interference pattern is observed.
Path difference
The difference in distance travelled by two waves from their sources to the point where they meet.
Constructive interference
is a path difference of nλ
Destructive interference
is a path difference of (n + ½)λ
Superimposing waves:
- Waves travelling same
direction we get a travelling wave. - Waves travelling opposite
direction we can get a standing wave ONLY if the waves have the same frequency.
Stationary waves:
- Continuous waves travelling in opposite directions will superimpose continuously, and this can set up a standing wave pattern.
- The waves need to be COHERENT (of the same speed, frequency,
similar amplitudes and have a constant phase relationship).
Stationary wave properties:
- The profile of the wave doesn’t move along – it only oscillates.
- Energy does not pass along a standing waves (it is NOT progressive
wave).
Progressive Wave
- Energy transferred in one direction.
- Max amplitudes at all points.
Standing/Stationary Wave
- Energy stored within a fixed system.
- Max amplitudes at specific points.
Nodes
superposition always fully destructive, amplitude is always zero, no vibration
Antinodes
points of maximum amplitude
Standing waves form on objects only when…
oscillated at resonant frequencies
Lowest frequency possible
fundamental frequency or 1st harmonic, f0
Higher frequency stationary waves are called…
2nd harmonics and have smaller and smaller wavelengths
string wavespeed
√t/u
f =
1/λ √t/u
f0 =
1/2L √t/u
Intensity of radiation
I = P/A
intensity of radiation is proportional to:
- Amplitude squared
- Frequency squared
spherical waves intensity of radiation
I = P/ 4π2^2
Assuming there’s no absorption of the wave energy, the intensity…
It decreases with increasing distance from the source.
Diffraction
The spreading out of a wave as it passes a gap aperture or passes around an obstacle
Maximum diffraction can be achieved if:
- the wavelength of the wave is equal to the size of the gap / obstacle
- the wavelength of the wave is equal to the size of the object / obstacle
wavefront
is the set of all locations in a medium where the wave is at the same phase. This could be where all the crests are, where all the troughs are, or any phase in between
Huygen’s principle is used…
to predict he movement of waves if we know the positions of a wavefront
To use Huygen’s principle, we consider:
- That every point on a wavefront is a new source of circular waves travelling forwards from that point
- After plotting numerous circular waves from the wavefront, we can consider superpositions to determine the new wavefront position
The tangents creates (diffraction)…
the curve of the new wavefront emerging wither through the gap or around the obstacle
A stable interference pattern forms when…
overlapping waves are coherent (constant phase difference) with one another
Interference patterns:
- Maxima - greatest amplitude - constructuve interface
- Minima - smallest amplitude - destructive interference
Refraction:
- Waves change speed as they cross boundaries between different mediums
- Wavelength changes during refraction but frequency stays the same
change in speed means…
change in wavelength
speed down –>
wavelength down
Speed up –>
wavelength up
Refractive index
the ratio of the speed of light in a vacuum to the speed of light in the medium
more ligh is refracted if…
there is a greater chnage in speed
the greater the refractive index –>
the greater refraction
Shorter wavelength / higher frequency refracted…
more strongly, wave speed slowed more
Critical angle
The angle of incidence (in denser medium) for which the angle of refraction (in less dense medium) is 90º
critical angles equation:
sin(c) = 1/n
Partial reflection
Both refraction and reflection occur but not equally
Total Internal Reflection:
- When light within a denser medium strikes a boundary with a less dense medium
- At an angle of incidence that is greater than the critical angle
- ALL of the light is reflected
Uses of Total Internal Reflection:
- Fibre optics
- Decorative lighting
- Fibre broadband
- Medical endoscope
Polarisation occurs…
when particles are only allowed to oscillate in one of the directions perpendicular to the direction of wave propagation
Polarisation cannot occur in…
longitudinal waves as they oscillate in the same direction as the direction of motion
A transverse wave can be polarised in 2 ways:
- Vertically polarised
- Horizontally polarised
Unpolarised Light:
- The oscillations of the electric/magnetic fields of an electromagnetic waves occur in all directions
- osciallte perpendicular to the direction of energy transfer
Polarised light:
- The oscillations of the electric / magnetic fields of an electromagnetic waves occur in only one plane
- Osciallate perpendicular to the direction of energy transfer
Partially-polarised waves:
Most oscillations near a single plane, e.g. reflections from surfaces
Light can be polarised by…
making them pass through a polarising filter (also known as a polariser)
A polariser with a vertical transmission axis…
only allows vertical oscillations to be transmitted through the filter
ligh is said to be partially polarised light if…
the intensity of light varies between maximum and minimum for every rotation of 90º of the analyser
Diffraction grating
is a large number of slits equally spaced. It will cause multiple diffraction patterns that superpose.
diffraction gratting equation
s = 1 / N
Electron diffraction:
- The electrons are accelerated in an electron gun to a high potential and then directed through a thin film of graphite
- Graphite film is ideal for this purpose because of its crystalline structure
- The diffraction pattern is observed on the screen as a series of concentric rings
larger accelerating voltage
reduces the diameter of a given ring
lower accelerating voltage
increases the diameter
The da Broglie Relation
- De Broglie theorised that not only do EM waves sometimes behave as particles, but that very small, fast-moving particles like electrons could also behave as
waves.
-
The de Broglie hypothesis states…
that all particles have a wave nature and a particle nature, and that the wavelength of any particle can be found using the following equation:
The greater the momentum… (da Broglie)
the smaller the de Broglie wavelength
What was the effect of changing the accelerating voltage of electrons on
the electron diffraction pattern?
- Higher energy and momentum result in a shorter de Broglie wavelength, allowing electrons to probe structures on a smaller scale (increases resolution)
- With a shorter wavelength, the waves are diffracted less and so the
diameters of the diffraction rings decrease.
Two-slit electron interference
- An interference pattern is built up by the movement through the
apparatus of the individual electrons. - Electrons behave as both individual particles and waves at the same time.
- Wave-particle duality!
Electron microscopy:
- Electrons’ de Broglie wavelength is shorter than the wavelength of light microscopes
- It can be made ever shorter by increasing speed and hence momentum
- The shorter the wavelength, the better the resolution in microscopes.
Electron microscopy
The shorter the wavelength, the better the resolution in microscopes.
The photon model
- Photons are fundamental particles which make up all forms of electromagnetic radiation
- The higher the frequency of EM radiation, the higher the energy of the photon
- The energy of a photon is inversly proportional to the wavelength
- A long-wavelength photon of light has a lower energy than a shorter-wavelength proton
Electron structure:
- Electrons in an atom orbit around the nucleus at particular distances, known
as energy levels - A certain number of electrons can occupy each energy level
- The higher the energy level, the further the distance of the electron from the nucleus
Atomic Line Spectra
- Electrons cannot stay in a continuous state of excitation, so they will move
back to lower energy levels through de-excitation - An emission line spectrum is produced when an excited electron in an atom moves from a higher to a lower energy level and emits a photon with an energy corresponding to the difference between these energy levels
- During de-excitation, energy must be conserved, so transitions result in an emission of photons with discrete frequencies
- Since there are many possible electron transitions for each atom, there are many different radiated wavelengths
- This creates a line spectrum consisting of a series of bright lines against a dark background
- An emission line spectrum acts as a fingerprint of the element
- Each element produces a unique emission line spectrum due to its unique set of energy levels.
line of the emission spectrum
- Each line of the emission spectrum corresponds to a different energy level transition within the atom
- Electrons can transition between energy levels absorbing or emitting a discrete amount of energy
- An excited electron can transition down to the next energy level or move to a further level closer to the ground state
Energy required to move from one energy level to another…
is given by the difference of energy between the two energy levels
A negative value for the energy implies…
that energy must be supplied to the system if the electron is to overcome the attractive force of the nucleus and escape from the atom.
The electron volt
The electronvolt is a unit of energy, susally used to express small energies
1eV is equal to…
The kinetic energy of an electron accelerated across a potential difference of 1V
Joules to eV
divide by 1.6 x10^-19
eV to joules
multiply by 1.6 x10^-19
Photoelectricity
- Where photoelectrons are emitted from the surface of a metal after light about
a certain frequency is shone on it. - Main evidence that light acts as a particle (photons)
