11 - Waves 1 Flashcards
What is a wave?
A physical phenomenon and that transfers energy through a medium without a transferring matter.
Waves travel or transfer energy through oscillations in a medium.
Either particles of a medium oscillate (mechanical wave)
OR electrostatic & magnetic fields in a medium vibrate (EM Waves)
What are the types of waves?
There are only two types of waves mechanical and EM
Transverse and longitudinal are modes of vibration - how vibrations happen with respect to direction of energy transfer
What is a transverse wave?
Waves in which the direction of oscillation is perpendicular to the direction of wave travel or energy transfer
Examples:
Waves on surface of water and electromagnetic waves
What is a longitudinal wave?
Wave in which direction of oscillation is parallel to the direction of wave travel (energy transfer).
Example:
Sound wave
Define displacement
The distance from the equilibrium position in a particular direction. Displacement is a vector, so it has a positive or negative value
Define amplitude
The maximum displacement from the equilibrium position (can be positive or negative)
Define wavelength
The minimum distance between two points oscillating in phase*. For example the distance from one pig to the next or from one compression to the next
- two adjacent vibrating particles/points with the same velocity at same displacement
DISTANCE BETWEEN 2 POINTS THAT ARE IN PHASE
Define period
Oscillations-the time taken for particle/point to complete one oscillation
Waves – time taken for one complete wavelength to pass a given point
Define phase difference
The difference between the displacement of particles along a wave (or on different waves)
Measured in degrees or radians
Each complete cycle or a difference of 1 wavelength representing 360° or 2 TT radians
Define frequency
Oscillations – number of complete oscillations per unit time. Hertz, Hz
Waves – the number of wavelengths passing a given point per time
Explain wave speed
The speed at which a wave travels through the medium is constant, and determined by properties of medium.
Thus, the higher the frequency of a given type of wave, the shorter its wavelength.
The speed is a fundamental property that changes when crossing between media, leading to change in wavelength (never frequency)
The wave equation
v = f x wavelength (aka lambda)
Speed of electromagnetic waves
3 x 10 ^8 m/s
Frequency and time period relationship
F = 1/T
Equation for speed of EM waves
c = f x wavelength (aka lambda)
Types of progressive waves
Transverse and longitudinal
How to use an oscilloscope to determine frequency?
A
Graphical representation of transverse & longitudinal waves
Transverse : wave with crests and troughs
Longitudinal : wave with compressions and rarefactions
What is the phase of a particle/ point ?
Fraction of a complete cycle/wave that a particle is at (at any given moment in time)
What is phase difference? And what types?
Difference in phase between 2 points along same wave or between 2 different waves at any given point in time.
What is phase difference measured in ?
Phase difference of 1 complete wave?
Radians, rad.
I complete wave = 2pi radians
General formula to calculate phase?
Fraction of wave completed x 2pi
How to calculate phase difference between 2 points on same wave ?
2 points, distance d apart, along wavelength (lambda):
Phase difference = (d/ lambda) x 2pi
How to calculate phase difference between 2 different waves, when they meet/ interact?
- at a given point in TIME, the difference between phases of each wave
Phase difference = (current phase in wave 1) - (current phase in wave 2)
In phase and antiphase in relation to phase difference ?
Define wavelength in terms of phase
- 2 points / waves are IN PHASE if their phase difference is an EVEN INTEGER of pi (2pi, 4pi etc)
- 2 points / waves are IN ANTIPHASE if their phase difference is an ODD INTEGER of pi (3pi, 5pi etc)
Wavelength of a wave is the distance between 2 adjacent points that are in phase.
What does being ‘in phase’ mean?
Same displacement from equilibrium and same velocity
Relationship between frequency and phase difference, wrt time?
- when 2 waves of SAME frequency meet at a point, as time MOVES FORWARD, phase difference is MAINTAINED/CONSTANT
- when 2 waves of DIFFERENT frequencies meet at a a point, as time MOVES FORWARD, phase difference changes over time (constantly cycling between 0 and 2pi)
What are wavefronts and why are they used?
Wave diagrams are required so we can define wave properties of amplitude, wavelength, frequency etc.
Wavefronts now required to explain the phenomena of reflection, refraction, diffraction and superposition
Wavefronts are lines of constant phase. These illustrate how a wave propagates. Change in wavefronts illustrates occurrence of some wave phenomenon
Wavefront in diffraction
When wavefronts approach a gap which is small relative to the wavelength, the wavefronts on the other side of the gap are circular (conversely, the wavefronts don’t change shape when approaching a gap with a size much larger than the wavelength of the incident waves).
Hence large wavelength soundwaves are able to diffract and fill a room, but small wavelength light is not.
Define reflection.
When a wave reverses direction upon meeting the boundary between two different media
Define law of reflection
Angle of incidence, i = angle of reflection, r
Define refraction
Refraction is when a wave changes direction upon crossing the boundary between two different media.
Speed changes, results in a change of wavelength. Frequency is a constant for a given wave
Explain reference in water waves. Refraction?
Wavefronts are travelling quickly in deep water and are quite spread out. Wavefronts travel slower and shallow water, and are closer together
Explain refraction at an angle to the normal?
If an incident wave approaches at a non-0 angle to the normal of the boundary, it also experiences a change in direction. This is explained by a part of the wavefront changing speed first.
Rules of refraction: speed, density
1) When slowing down,
Bend towards normal
Wavelength gets shorter
When speeding up,
Bend away from normal
Wavelength gets longer
2) Sound waves speed up going into physically denser mediums
EM waves slow down going into optically more dense media
Physical density vs optical density
Physical density – measure of how much mass per unit volume
Optical density – measure of how much light is slowed down inside a medium
Define intensity
Power per unit area
Intensity equation
I = P/A
Or I = P/ 4pi r^2
(SA of sphere = 4pi r^2 )
Relationship between intensity & distance
Waves (from a point source) spread out as they travel outwards.
Intensity falls as power of source is spread over INCREASING area
Area over which power is spread out = SA of sphere of radius equivalent to distance travelled from source
Exact relationship between distance & intensity (USING KEY WORDS)
Intensity of wave follows an inverse square relationship wrt distance travelled by source
Relationship between intensity & amplitude ?
Intensity is proportional to amplitude ^2
What is the EM spectrum?
A continuum of all the EM waves, ordered by frequency / wavelength
State the waves in order of reducing wavelength (increasing frequency)
Radio waves, microwaves, infrared, visible, UV, X rays, Gamma Rays
Wavelength of radio waves
> 10^6 to 10^-1
Wavelength of microwaves
10^-1 to 10^-3
Wavelength of infrared
10^-3 to 7x10^-7
Wavelength of visible light
700 nm to 400 nm
7x10^-7 to 4x10^-7
Wavelength of UV
4x10^-7 to 10^-13
Wavelength of Gamma rays
10^-10 to <10^-16
slight overlap with x rays
In a prism, visible white light enters and splits into its different components. What does this look like and why?
ROYGBIV from top to bottom
V refracts most because it has the smallest wavelength, so slowest speed (?)
Vice versa for red
Properties of EM waves
- reflect
- refract
- diffract
- superpose
- be polarised
- All EM waves travel @ SAME SPEED in ONLY through VACUUM
In other media, speed changed wrt the frequency
Define diffraction
Physical phenomenon of waves spreading out when passing through a gap, or around an obstacle
What are the rules of diffraction
The narrower the gap, the more the waves spread out
The longer the wavelength, the more the waves spread out
The smaller the gap relative to the wavelength of the incident waves, the greater the diffraction. Gap size has to be of similar or same order of magnitude as wavelength for significant diffraction to occur
Wave speed & wavelength do not change upon diffraction
What is polarisation
A property of transverse waves, which defines the plane of oscillation of the wave.
The plane of polarisation of an EM wave is defined as the plane in which the electric field vibrates
Are EM waves unpolarised?
Most sources of light (natural or man-made) generate unpolarised EM waves.
Unpolarised light consists of wave-trains within which different waves have their E-field aligned in different planes
How can EM waves be polarised?
- absorption (Polaroid filters)
2. reflection (glare, sunglasses)
Explain how light is polarised with filters
The plane of alignment of a Polaroid filter is the plane in which it will allow the E-field oscillations to pass through. The transmitted light is then polarised in the SAME plane.
The filter allows through components in the same plane as its alignment, of all waves.
If the plane of polarisation of incident wave matches plane of alignment of the filter, 100% of wave is transmitted.
If @ some angle, theta, to the plane of alignment of filter, <100% of wave transmitted. Transmitted intensity is Proportional to cos^2(theta)
If perpendicular to the plane of alignment of filter, 0% of wave transmitted
Explain how light is polarised with reflection
- Light reflected off metal surfaces and water is mostly polarised in the HORIZONTAL plane
- Sunglasses have VERTICALLY aligned Polaroid filters in order to block all horizontally plane polarised light from reaching the eye. This reduces bright colour without huge reduction in background light intensity
What is refractive index
The refractive index of a medium is a ratio between the speed of light in a vacuum, c, to the speed of light in that medium, v
Formula of the refractive index
n = c / v
Smallest refractive index is 1.00
Relationship between speed in a medium and refractive index
INVERSELY PROPORTIONAL
The greater the DECREASE in speed in a medium, The greater the refractive index of the medium, The more light refracts in that medium
Relationship between the refractive index of a medium and the angle of incidence and refraction & when does it work?
n = sin i / sin r
Only holds true when light is INCIDENT in a VACUUM and REFRACTS into a MEDIUM of refractive index n
1/n = sin i / sin r
If light is incident in a medium of refractive index n, and refracts into a vacuum
State & define Snell’s Law
In general (when the vacuum is not one of your media) when light passes between 2 media of different refractive indices, light refracts according to the relationship below:
n1sin(theta1) = n2sin(theta2)
Define total internal reflection
Wave phenomenon by which light completely reflects back @ a boundary between 2 media, instead of transmitting across the boundary and refracting
Conditions needed for total internal reflection to occur
- Medium within which light is INCIDENT has a larger refractive index, n than second medium
- Angle of incidence EXCEEDS critical angle, i c for a given medium
What is the angle of refraction at the critical angle?
90 degrees
Ray travels along boundary
What happens when
theta < C
theta = C
theta > C
theta < C ; refraction + partial reflection
theta = C ; light refracts along boundary between 2 media
theta > C ; total internal reflection
How to calculate critical angle
sin(theta c) = n2 / n1
should be between -1 to 1
Critical angle of a given medium in air / vacuum is?
sin (theta c) = 1 / n
Refractive index of diamond
- v high refractive index : 2.42
- disperses white light a lot
- has small critical angle, 24 degrees. Light totally internally reflected many times, so disperses even more
Refractive index of optical fibres
- used in endoscopes to see the inside of the body and in communications to send signals
- light is always incident at the fibre boundary @ angle GREATER than the critical angle so the light is constantly totally internally reflected
- fibres are highly transparent to minimise absorption of light which would lead to loss of signal.
- core must be v narrow to prevent modal (multipath) dispersion. Would occur if there was a significant pathlength difference between rays going straight down core & those that are reflected off core cladding boundary
Polarisation in aerials
In order to reduce interference between different communication transmitters, some transmit vertically plane polarised waves and others nearby transmit horizontally plane polarised waves.
An aerial aligned to detect vertically polarised radio waves will suffer less interference from horizontally polarised waves, and vice versa
Transmission and intensity of polarised wave at an angle to filter alignment?
If @ some angle, theta, to the plane of alignment of filter, <100% of wave transmitted.
Transmitted intensity is Proportional to cos^2(theta)
