C11-12. Waves Flashcards
Define a progressive wave.
This is a wave that transfers energy, causing the particles of the medium it travels through to oscillate about a fixed position.
What is a transverse wave?
A wave in which particles oscillate perpendicular to the direction of wave propagation.
What is a longitudinal wave?
A wave in which particles oscillate in parallel to the direction of wave propagation.
What is displacement?
The distance of a point on a wave from its equilibrium position.
What is amplitude?
The maximum displacement of a particle from its rest position.
What is wavelength?
The minimum distance between adjacent points oscillating in phase on a wave.
What is time period?
The time taken for one full wave cycle to be completed.
What is frequency?
The number of complete cycles passing a point per unit time.
How do we define phase difference?
The difference in displacements of particles along a wave.
What units are usually used for phase difference?
Degrees or radians, or metres.
What do we mean if we say two particles are in-phase?
Both particles reach their maximum displacement at the same time - they oscillate in-step.
What do we mean if we say two particles are in antiphase?
Both particles oscillate completely out of step, so as one reaches its maximum positive displacement, the other reaches its max. minimum displacement.
What is the phase difference between two particles in-phase generally?
Either 0 or an even integer coefficient of pi radians.
What is the phase difference between two particles oscillating in anti phase generally?
An odd integer coefficient of pi radians.
What equation links frequency, wavelength and wave speed?
v=f*lambda
Define reflection.
When a waves changes direction at a boundary between two media, remaining in the original medium.
State the law of reflection.
When 2 waves are reflected, the angle of incidence is always equal to the angle of reflection.
Define refraction.
When a wave changes direction as it passes through one medium into another.
If a light wave enters a more dense medium, what can we say about its new speed and direction?
It will travel more slowly, and its angle of refraction will be closer to the normal line.
If a light wave enters a less dense medium, what can be said about its new speed and direction?
It will travel more quickly, and its angle of refraction will be further from the normal line.
Why doesn’t reflection affect wavelength?
Reflection does not impact wave speed or frequency, so has no impact on wavelength.
How is wavelength affected by entering a denser medium?
Wavelength decreases, and frequency remains unchanged.
Define diffraction.
The process in which a wave spreads out when it passes through an aperture.
This effect is most prominent when the slit/gap is around the same size as the wavelength.
When does total internal reflection occur?
This occurs when the angle of incidence is such that the angle of refraction becomes 90 degrees.
This angle of incidence is then called the critical angle.
What is the critical angle?
The angle of incidence at which total internal reflection occurs.
What happens to a wave when total internal reflection occurs?
it is strongly reflected back into its original medium.
What is refractive index, and how can we calculate it?
A property of a material showing how much light slows down when passing through it.
n=C/v
How does a material being optically dense affect the way light transmits through it?
An optically dense material has a higher refractive index, so light travels slower through it.
How are refractive index and speed of light in a medium related?
As refractive index increases above 1, speed of light within the material falls.
What equation represents Snell’s Law?
n1sin(incidence)=n2sin(refraction)
How can we derive the refractive index equation for critical angle?
sin(critical angle)=1/n
Define intensity of a wave, and give a general equation for it.
The radiant power passing through a surface per unit area.
I=P/A
Give an equation for the radiant power from a point source.
I=P/4(pi)r^2
This is because the the surface area of a sphere = 4(pi)r^2.
How is the intensity of a wave linked to its amplitude?
Intensity is proportional to the square of amplitude.
I=kA^2
What can we say about the relationship between distance from a point source and intensity?
For a given power, radiant power spreads out as we move further away from the source, reducing intensity.
The relationship is inversely proportional.
What is polarisation?
When particle oscillations occur along a single plane only - this plane also contains the direction of wave oscillation.
A polarised particle is said to be plane polarised.
Why can polarisation only occur in transverse waves?
When we polarise a transverse waves, we restrict its electric field oscillations to a direction perpendicular to that of propagation.
In longitudinal waves, these are parallel, so polarisation cannot occur. Oscillations are already limited to one plane.
Why does partial polarisation occur when a wave reflects from a surface?
There are more waves oscillating in a given plane, but not all, so the wave is not entirely plane polarised.
What methods can we use to polarise a wave?
Light waves: a polarising filter.
Microwaves: a metal grille.
How do polarising filters work?
Where the direction of electric field oscillation is parallel to to that of the transmission axis, these waves can pass through, and intensity increases.
Waves with perpendicular oscillations are not transmitted, so intensity is reduced.
How are most EM waves naturally found, in terms of polarisation?
From their source, Em waves are generally unpolarised, so oscillations occur at 90 degrees to the direction of propagation in random planes.
How do we use metal grilles to polarise microwaves?
Free electrons in the metal grille fully absorb the electric field oscillating in the same direction as the grille and intensity falls.
Where the electric field oscillates at 90 degree to the direction of the grille, the wave can pass and intensity increases.
What is the difference between polarising EM wave with a filter and with a metal grille?
With a filter, waves are transmitted if oscillations are parallel to the transmission axis. With a grille, waves are transmitted if oscillations are perpendicular to the grille.
How are polarisers used in aerial communications?
A transmitter broadcasts a plane-polarised signal which then travels towards an aerial. The aerial will only detect waves polarised in the direction it is aligned. This reduces interference.
What properties do all electromagnetic waves have?
- They are all transverse
- They can all travel in a vacuum
- They all travel at the same speed in a vacuum - the speed of light (3x10^8 ms-1)
What two components form an electromagnetic wave, and how are they arranged?
They have electric and magnetic fields oscillating perpendicular to one another and to the direction of wave propagation.
What 7 types of EM wave make up the electromagnetic spectrum? Order them from lowest-highest frequency.
- Radio waves
- Microwaves
- Infrared
- Visible light
- UV
- X-rays
- Gamma rays
What is the effect of frequency on radiation energy?
As frequency increases, so does the energy of radiation. High radiation energies are particularly ionising, so can be harmful to tissues.
What is the principle of superposition?
When two waves of the same frequency meet at a given point, the sum of their individual displacements at that point is equal to that of the resultant wave they form.
What is interference?
The process in which two progressive waves overlap to form a resultant wave as per the principle of superposition.
When does constructive interference occur?
When 2 waves superpose in phase, so their maximum and minimum displacements line up.
When does destructive interference occur?
When two waves superpose in anti phase, so one waves’ maximum displacement lines up with the others’ minimum.
What is constructive interference?
When 2 progressive waves superpose in phase and interfere to produce a larger resultant displacement.
What is destructive interference?
When 2 progressive waves superpose in anti phase to produce a smaller resultant displacement.
What phenomenon occurs when two waves of the same frequency AND amplitude superpose in anti phase?
They interference destructively and entirely cancel one another out.
How is displacement linked to intensity?
- The greater the maximum displacement achieved by oscillating particles, the higher the amplitude.
- Intensity is proportional to the square of amplitude so rises exponentially.
How is a stationary wave formed?
Two coherent waves following a constant-phase relationship must travel towards one another along the same line of propagation.
What defines coherent waves?
They have the same frequency and wavelength.
What is an interference pattern?
The arrangement of maxima and minima formed due to the constructive and destructive interference of coherent waves.
Define maxima.
A point at which constructive interference occurs in an interference pattern.
Define minima.
A point at which destructive interference occurs in an interference pattern.
What is path difference?
The difference in the distance travelled by two interfering waves from their respective sources.
If path difference is an integer multiple of wavelength, what can we say about interference where the waves meet?
The waves meet in phase so constructive interference occurs, giving rise to the formation of a maxima.
If path difference is an integer+1/2 multiple of wavelength, what can we say about interference where the waves meet?
The waves meet in anti phase so destructive interference occurs, giving rise to the formation of a minima.
How does path difference link to phase difference?
- For an (integer multiple of wavelength) path difference, phase difference is an even multiple of pi.
- For an (integer+1/2 multiple of wavelength) path difference, phase difference is an odd multiple of pi.
Describe Young’s slit experiment.
- A monochromatic source of light waves is passed through a double slit
- This essentially produces two coherent sources of waves
- These superpose along a screen with different path differences to form maxima and minima
What equation links wavelength, slit operation, fringe separation and distance?
lambda=ax/d
What two features characterise a stationary wave?
Nodes, areas of zero displacement, and antinodes, areas of maximum displacement.
Define phase difference in terms of superposition.
The difference in phase between two waves arriving at the same point.
Describe phase differences in a stationary wave.
- Between adjacent nodes all particles oscillate in phase
- Either side of a node, particles oscillate in antiphase
How might we produce and detect a stationary wave from microwaves?
- Aim a source at a reflecting surface
- The wave that is reflected will interfere with the original wave to form a stationary wave
- Move a detector along the line of propagation to detect nodes (min. intensity) and antinodes (max. intensity)
How might we produce a stationary wave in a taut string?
- Use a signal generator to produce oscillations in a string held taut at the other end.
- Waves will reflect from the other end to form a stationary wave.
- Nodes form at either end and possibly in-between depending on the harmonic formed.
What is the fundamental frequency, f0?
The lowest frequency at which something can oscillate. This is dependent on the position of (anti)nodes at each end.
What is another name for the first harmonic?
The fundamental mode of vibration - essentially where the fundamental frequency f0 is achieved.
What is a harmonic?
A stationary wave whose frequency is an integer multiple of the fundamental frequency, nf0.
How can stationary waves be formed by longitudinal waves like sound?
A sound wave propagates before being reflected and superposing with the original wave.
How are stationary waves formed in a tube?
The wave makes air in the tube oscillate about a fixed position, forming nodes and antinodes at closed and open ends.
Why are nodes formed at a closed end of a tube?
Particles cannot oscillate at the closed end, so zero resultant displacement occurs and a node if formed.
Why is an antinode formed at the open end of a tube?
Maximum displacement can be achieved by oscillating air particles.
Why can only certain harmonics with odd integer multiples of f0 form in a tube closed at one end?
A node must form at one end and an antinode must form at the other. This limits the shape of the stationary waves that form.
Why can only certain harmonics with even integer multiples of f0 form in an open-ended tube?
Antinode must form at both ends of the tube. Therefore this limits the combinations of nodes and antinodes in a stationary wave that can form.
How do we generally form a stationary wave?
- Coherent progressive waves with a constant -phase relationship superpose.
- Where they are in anti phase, minimum displacement occurs and a node is formed.
- Where they are in phase, maximum displacement occurs and an antinode forms.
How can we use v=f*lambda to determine the frequency of harmonics?
- In harmonics, wavespeed is always unchanged.
- However, wavelength is always some relation to the original length of the tube based on the number of nodes and antinodes.
- We can use this idea to determine frequency.
How does energy transfer differ in stationary vs. progressive waves?
- Stationary: no net energy transfer as wave move in opposite directions. Energy is stored
- Progressive: energy transfers in direction of propagation
How does phase difference differ in stationary vs. progressive waves?
- Stationary: between nodes particles oscillate in phase, either side in anti-phase
- Progressive: phase changes continuously across a complete cycle. Particles in adjacent cycles in the same position are in phase
How does amplitude differ in stationary vs. progressive waves?
- Stationary: max. amplitude at antinode and min. at node
- Progressive: amplitude is the same throughout as all particles reach the same max. displacement at some point
