Module 4: C11 - Waves 1 Flashcards
What is a Progressive Wave
A progressive wave is a means of transferring energy from one place to another without a transfer of matter between the two points.
What are the 2 types of Progressive Waves
There are two types of progressive wave; a transverse wave and a longitudinal wave.
What are Transverse Waves
Transverse waves are waves where the direction of oscillation of a wave is perpendicular to the direction of motion of the wave.
(Transverse waves have peak and troughs where the oscillating particle are at a maximum displacement from their equilibrium position.)
What are Longitudinal Waves
Longitudinal Waves are waves where the direction of oscillation of a wave is parallel to the direction of motion of the wave.
Explain what is meant by a progressive wave
A progressive wave is where energy is transferred from one place to another without a transfer of matter between the two points. (They can transfer energy and information)
Describe, in terms of vibrations, the difference between a longitudinal and transverse wave. Give one example of each wave
Transverse waves are waves where the direction of motion is perpendicular to the oscillation of the wave (such as light waves), meanwhile longitudinal waves are waves where the direction of motion is parallel to the oscillation of the wave (such as sound waves and P-waves)
What are examples of Transverse Waves
- Waves on the surface of the water
- Any electromagnetic wave - radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
- Waves on stretched strings
- S-waves produced in earthquakes
What are examples of Longitudinal Waves
- Sound waves
- P-waves produced in earthquakes
What happens with Longitudinal waves when they travel through a medium
Longitudinal waves are often called compression waves. When they travel through a medium they create a series of compressions and rarefactions.
Displacement:
- Symbol
- Unit
- Definition
Symbol:
s
Unit:
m
Definition:
Distance from the equilibrium position in a particular direction; a vector, so it can have either positive or negative value.
Amplitude:
- Symbol
- Unit
- Definition
Symbol:
A
Unit:
m
Definition:
Maximum displacement from the equilibrium position (can be positive or negative)
Wavelength:
- Symbol
- Unit
- Definition
Symbol:
λ
Unit:
m
Definition:
Minimum distance between two point in phase on adjacent waves, for example, the distance from one peak to the next or from one compression to the next.
Period of Oscillation:
- Symbol
- Unit
- Definition
Symbol:
T
Unit:
s
Definition:
The time taken for one oscillation or time taken for wave to move one whole wavelength past a given.
Frequency:
- Symbol
- Unit
- Definition
Symbol:
f
Unit:
Hz
Definition:
The number of wavelengths passing a given point per unit of time
Wave Speed:
- Symbol
- Unit
- Definition
Symbol:
v (or c)
Unit:
ms^-1
Definition:
The distance travelled by the wave per unit of time
Wave Equation (involving frequency, wave length, and wave speed)
Wave Speed = Frequency x Wavelength
v = f λ
What is a Wave Profile
A graph showing the displacement of particles in the wave against the distance along the wave is called wave profile.
What can the Wave Profile be used to determine in a wave
The wave profile can be used to determine the wavelength and amplitude of both types of waves. As the displacement of the particle in the wave is continuously changing, the wave profile changes shape over time.
Worked Example: Finding the wavelength of a musical note
A flute produces a high-pitched note that has a time period of 0.45ms. The speed of sound through air is 330ms^-1. Calculate the wavelength of the note produced.
Step 1: Identify the correct equation to calculate the speed of the wave.
v = f λ
As f = 1/T substituting into the first equation gives v = λ/T => λ = vT.
Step 2: Substitute in known values in SI units and calculate the wavelength of the note.
λ = 330 x 0.45x10^-3 = 0.15m
What is Phase Difference
Phase difference describes the difference between the displacements of the particles along a wave, or the difference between the displacements of the particles on different waves.
Note: It is most often measured in degrees or radians.
What is the equation for Phase Difference
Phase Difference ϕ = 2π x/ϕ
What is Phase Difference
Phase difference describes the difference between the displacement of particles along a waves or the difference between the displacements of particles on different waves. It is most often measured in degrees or radians, with complete cycle or wave representing 360° or 2 π radians
What does it mean when Particles are described as being ‘in Phase’
If particles are oscillating perfectly in step with each other (they both reach their maximum positive displacement at the same time) then they are described as in phase. They have a phase difference of zero.
If two particles are separated by a distance of one whole wavelength, we say their phase difference is 360°, or 2π radians. If they are two complete cycles out of step their phase difference is 720° or 4 π radians.
What does it mean when Particles are described as being ‘in Antiphase’
If particles are oscillating completely out of step with each other (one reaches its maximum positive displacement at the same time as the other reaches its maximum negative displacement) then they are described as being antiphase. They have a phase difference due of 180°, or π radians.
Two particles can have any phase difference as a phase difference depends on the separation of particles in terms of the wavelength.
What is the Law of Reflection?
The law of reflection applies whenever waves are reflected. It states that the angle of incidence is equal to the angle of reflection.
What is Reflection
Reflection occurs when a wave changes direction at a boundary between two different media, remaining in the original medium. Example: mirrored surface.
The law of reflection:
The angle of incidence is equal to the angle of reflection when measured to the normal.
What is Refraction?
Refraction occurs when a wave changes direction as it changes speed when it passes from one medium to another.
The amount of refraction depends on the refractive index of the material.
How does the Refraction of Water Waves affect Wave Speed and Wavelength?
The speed of water waves is affected by changes in the depth of the water, which gives us an easy way to investigate the refraction of water waves. When a water wave enters shallower water, it slows down and the wavelength gets shorter
Why do wave refract towards and away from the normal?
If a wave slows down it will refract towards the normal, if it speeds up it refracts away from the normal. Sound waves normally speed up when they enter a denser medium, whereas electromagnetic waves, like light, normally slow down. This results in the waves refracting in different directions.
Equation for Refractive Index
n = c/v
(Refractive Index = Speed of Light in Vacuum / Speed of Light in Material)
Where n is the refractive index of the material (it has no units), c is the speed of light through a vacuum (3.00x10^8) and v is the speed of light through the material in ms^-1
If n=1 then the speed of light through the material is the same as the speed of light through a vacuum.
Equation to show what happens when light travels from one medium to another
n1sinΘ1 = n2sinΘ2
Worked Example: The speed of light through Olive Oil
Determine the speed of light through Olive Oil
(For Olive Oil, n=1.47)
Step 1: Identify the correct equation.
n = c/v
v = c/n
Step 2: Substitute in known values in SI units and calculate the speed of light through the Olive oil.
v = 3.0x10^8 / 1.47 = 2.04x10^8ms^-1
The speed of light through the material will always be less than the speed of light through a vacuum.
Worked Example: Calculating the angle of Refraction
A ray of light travels from water to crown glass. The light strikes the boundary between the two at an angle of 40.0° to the normal. Calculate the angle of refraction.
(For down glass, n=1.52)
Step 1: Identify the correct equation
n sin Θ = k
Apply this equation to a ray of light travelling from water into glass.
n.water sinΘ.water = n.glass sinΘ.glass
Rearrange for sinΘ.glass
sinΘ.glass = (n.water sinΘ.water) / (n.glass)
Step 2: Substitute in known values and calculate sinΘ.glass
sinΘ.glass = [1.33 x sin(40)] / 1.52 = 0.562…
Θ.glass = 34.2°
This angle is less than 40.0°, as the light has slowed down when it entered the glass from the water, bending towards the normal.
What is the Special case if the Refraction Law
n = sinΘ1 / sinΘ2
Equation made by Snellius (Snell’s Law)
n sinΘ = k
Example Question:
The speed of light in ethanol is measured as 220x10^6ms^-1. Calculate the refractive index of ethanol.
n = 3x10^8 / 220x10^6
n = 1.36
Example Question:
A ray of light travels from diamond into water. The light strikes the boundary between the diamond and the water at 20°C. Calculate the angle of refraction.
(Diamond: n = 2.42
Water: n = 1.33)
n1sin(Ø1) = n2sin(Ø2)
2.42 sin(20) = 1.33 sin(Ø)
0.622 = sinØ
Ø = 38.5°
What is Diffraction
The spreading out of a wave as it passes through an gap/aperture or when they encounter an obstacle is called diffraction.
The speed, wavelength, and a frequency of a wave do not change when diffraction occurs.
When will Diffraction occur
Diffraction will only occur if the wavelength of the wave is of a similar size to the size of the gap/aperture.
What is the difference between refraction and diffraction?
Refraction occurs when a wave changes direction as it changes speed when it passes from one medium to another, whereas diffraction is when a wave spreads out after passing through a gap when there is an obstruction in the way (but doesn’t change direction).
What condition ensures that diffraction is increased?
Diffraction is increased when the size wavelength is closer to the size of the gap/aperture in the obstruction.
What is Polarisation
Polarisation means that the particles oscillate along one direction only, which means that the wave is confined to a single plane.
What is Unpolarised Light?
Light which oscillates in many different planes.
What is Polarised Light?
Light which oscillates in one plane only
Why can’t Longitudinal Waves be Polarised?
In longitudinal waves, the oscillations are always parallel to the direction of energy transfer, so longitudinal waves cannot be plane polarised. Their oscillations are already limited to only one plane (the direction of energy transfer)
What type of wave can be Polarised
Transverse Waves
Explain why electromagnetic waves can be polarised but sound waves cannot be polarised
Electromagnetic waves can be polarised, but sound waves cannot, as they are longitudinal waves, where the oscillations are always parallel to the direction of energy transfer, meaning they can’t be polarised.
(Only transverse waves can be polarised)
How does Partial Polarisation take place
Unpolarised light can also undergo polarisation by reflection off of non- metallic surfaces. The extent to which polarisation occurs is dependent upon the angle at which the light approaches the surface and upon the material that the surface is made of.
Non-metallic surfaces such as asphalt roadways, snowfields and water reflect light such that there is a large concentration of vibrations in a plane parallel to the reflecting surface. A person viewing objects by means of light reflected off of non-metallic surfaces will often perceive a glare if the extent of polarisation is large.
Why is it not possible to polarise a sound wave?
You can’t polarise a sound wave, as it is a longitudinal wave, where the oscillations are already always parallel to the direction of energy transfer. (Sound Waves & P-Waves)
Explain why the diffraction of sound is regularly observed, but the diffraction of light is observed less frequently
This will be because sound waves have a larger wavelength compared to visible light, meaning sound waves are more likely to meet gaps similar in size to it’s wavelength, therefore it’s will diffract more often.
Explain why it is possible to revive long-wavelength radio signals at the bottom of some valleys in which the higher-frequency TV signal cannot be received?
Long wavelength radio signals can be diffracted around valleys, allowing them to reach most areas, as the gap of the valley is a similar size to length of the wave. Therefore longer wavelength signals can be received better than shorter wavelength signals that would not diffract as easily.
What is Intensity
Intensity is the radiant power passing through a surface per unit area measured in Wm-2.
I = P/A
Equation for Intensity
Intensity = Power / Area
I = P/A
Calculate the intensity when a power of 400 W is received over a cross-sectional area of 20m^2
I = P/A
P=400W
A=20m^2
400/20 = 20
Intensity = 20Wm^-2
What is the relationship between Intensity and Distance (using the Intensity Equation)
The total radiant power P at a distance r from the source is spread out over an area equal to the surface area of the sphere (A = 4πr^2).
I = P/A
I = P/4πr^2
Therefore the relationship between Intensity and Distance follows the Inverse Square Law
Worked Example: Finding the Power of the Sun
What is the total power output of the Sun if the intensity of radiation received by the upper atmosphere is 1400 Wm-2? The average distance between the Earth and the Sun is 150 million km.
Step 1: Identify the correct equation to calculate the power from the Sun.
I = P/A = P/4πr^2
Step 2: Rearrange to make the power the subject
P = I x 4πr^2
Substitute in known values:
P = 4000 x 4π x (150x10^9)^2 = 4.0x10^26 W.
How can you tell there is an Inverse Square Relationship between Intensity and Distance from the Equation
I = P/4πr^2
We can see from the equation that the intensity has an inverse square relationship with the distance from the source (I∝1/r^2). If the distance doubles, the intensity decrease by a factor of 4 (2^2), and if the distance increases by a factor of 100 the intensity will be 100^2 times smaller.
Relationship between Intensity and Amplitude
Intensity ∝ (Amplitude)^2
How are Intensity and Amplitude related (+what is their relationship)
When ripples travel out across the surface of a pond the intensity drops as the energy becomes more spread out. This causes a drop in amplitude. That is, the ripple height decreases the further the wave is from the source.
Decrease amplitude means a reduced average speed of the oscillating with half the speed, and a quarter of the kinetic energy (Ek = 1/2mv^2). So for any wave the intensity is directly proportional to the square of the amplitude. Double the amplitude of a wave and the intensity will quadruple.
Intensity ∝ (Amplitude)^2
What are the 4 Properties of Electromagnetic Waves
● All EM waves travel at the speed of light. (In a vacuum
c = 3.0 x 108 ms-1) Therefore the wave equation for EM waves is: c=f𝝀
● EM waves can travel through a vacuum, no medium is required to travel through.
● EM waves with high frequency have high energy
● They are all transverse waves
State two properties shared by all electromagnetic waves which distinguish them from other waves.
All EM waves travel at the speed of light (3x10^8ms^-1), and they are able to travel in a vacuum, meaning no medium is required for them to travel.
Also EM waves with high frequency also have high energy too
Worked Example:
A radio station transmits at a frequency of 107.3MHz. Calculate the wavelength of the radio wave to an appropriate number of significant figures.
Step 1: Identify the correct equation to calculate the speed of the wave.
Rearranging this equation for λ gives
λ = c / f
Step 2: Substitute in the known values in SI units and calculate the wavelength.
λ = 3x10^8 / 107.3x10^6 = 2.80m (3sf)
Order of the EM spectrum from highest wavelength to lowest
In order of reducing wavelengths λ
Radio Waves >10^6 - 10^-1
Microwaves 10^-1 - 10^-3
Infrared 10^-3 - 7x10^-7
Visible Light 7x10^-7 - 4x10^-7
Ultraviolet 4x10^-7 - 10^-8
X-Rays 10^-8 - 10^-13
Gamma Rays 10^-10 - <10^-16
The wavelength ranges of which two rays overlap?
X-rays and gamma rays overlap at a certain point.
At this point they are classified on where they come from
Example Question:
The human eye can detect EM waves with wavelengths from around 400 to 700nm. Calculate the minimum and maximum frequencies of light that the eye can detect.
λ = 700 x 10^-9
c = fλ
f = c/f
3x10^8 / 7x10^-7 = 4.3x10^14 Hz
λ = 400 x 10^-9
c = fλ
f = c/λ
3x10^8 / 4x10^-7 = 7.5x10^14Hz
Therefore, the human eye can detect frequencies between 4.3x10^14 - 7.5x10^14
Example Question:
The Earth is on average 150 million km from the Sun. Calculate the time taken for light to travel from the Sun to the Earth.
c = 3x10^8ms^-1
s = d/t => t = d/s
1.5x10^11 / 3x10^8 = 500 seconds
What is a use for Polarisation of electromagnetic waves?
One use of the polarisation of electromagnetic waves is in communications transmitters. In order to reduce interference between different transmitters, some transmit vertically plane polarised waves and other 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.
How do Polarising Filters work?
Polarised electromagnetic waves can be polarised using filters called polarisers. The nature of the polariser depends on the part of the electromagnetic spectrum to be polarised, but each filter only allows waves with a particular orientation through.
- What is Malus’ Law
The intensity of a beam of plane polarised light after passing through a rotatable polarised varies as the square of the cosine of the angle through which the polariser is rotated from the position that gives maximum intensity.
Equation for Intensity (involving cos)
I = Io cos^2 Θ
When using 3 polarising filters, observe what happens when:
a) Filter 1 and 3 in the same plane, rotate filter 2
b) Filter 1 and 3 at 90° to each other. Rotate filter 2
a) When this happens you can see more
b) The light intensity decreases and you can’t see anything
Example Question:
A plane polarised radio wave is transmitted from a vertical aerial to a nearby receiving aerial.
The entire receiving aerial is rotated slowly through 180° in the direction shown by the arrow. Explain clearly what will be observed on the ammeter and how the detected signal varies.
From 0-90° the current will decrease before fall to 0 at 90°, as Malus’ Law states that I = Iocos^2Ø, where cos^2(90)=0, before the current starts to increase from 90-180°, where it reaches its maximum at 180°, where cos^2(180) = 1.
What happens when you place 2 Polaroid filters over each other and rotate them?
Unpolarised light passing through the first filter becomes plane polarised. If the second filter (sometimes called the analyser) is in the same plane as the first, then the light passes through it unaffected. However, if the second Polaroid is slowly rotated the intensity of the light transmitted through it drops. When the second filter has turned through 90°, no light is transmitted and the intensity falls to zero.
A metal grille is placed between a source of plane polarised microwaves and a receiver. Describe and explain the effect of rotating the grille through 180° around the axis of the beam on the intensity recorded by the receiver
As the grille is rotated the intensity falls.
It falls to zero when the gaps in the grille are in the opposite plane to the microwaves (after 90°).
As the grille is rotated further the intensity creases again.
It reaches the maximum value again when the gaps in the grille are in the same plane as the microwaves (after 180°).
Suggest why the metal sheet in the door of microwave ovens contains little holes, rather than a series of slits.
Holes will not allow any orientation of plane polarised microwaves through.
A student holds a polarising filter in front of a laptop screen and then rotates it. At a particular angle, the laptop screen appears to go dark.
a) Suggest what you can deduce about the nature of light emitted from the laptop screen from the student’s observation
b) Explain how the laptop screen can be viewed once again through the filter
a) It must must be plane polarised
b) Rotate the Polaroid further until it is at 90° from the minimum intensity.
In this orientation the Polaroid is aligned in the same plane as the light emitted from the screen.
Example Question:
A beam of polarised light is directed normally at a polarising filter of cross-sectional area 9.0x10^-4m^2. The polarising filter is slowly rotated in a plane at right angles to the beam. The transmitted intensity, I, plotted against the angle Ø resembles figure 3 with a maximum intensity of 20Wm^-2
a) Calculate the power of light transmitted through the filter at Ø = 0°.
a) 20 x 9.0x10^-4 = 1.8x10^-3 W
What is Total Internal Reflection (TIR)
The total internal reflection (TIR) of light occurs at the boundary between two different media. When the light strikes the boundary at a large angle to the normal, it is totally internally reflected. All the light is reflected back into the original medium. There is no light energy refracted out of the original medium.
What are the 2 Conditions required for Total Internal Reflection (TIR)
● The original material must have a higher refractive index than the surrounding material. (e.g. glass to air will cause TIR)
● The angle of incidence must be greater than the critical angle.
What is the Critical Angle
Critical angle: The angle of incidence at the boundary between two media that will produce an angle of reflection of 90°.
By using n1Sinθ1 = n2Sinθ2 , determine the relationship between the refractive index of the medium and the critical angle when light travel into air
At the critical angle C, θair is 90°
n sinC = nair sin90°
Both the refractive index of air and sin90 are equal to 1, so this becomes
n sinC = 1x1
sinC = 1/n
From this we can see that the greater the refractive index the lower the critical angle.
Equation to find the Critical Angle
SinC = 1/n
Worked Example: Crown Glass
Crown glass has a refractive index of 1.52. Determine the critical angle between crown glass and air.
Step 1: Identify the correct equation to use.
Sin C = 1/n => C = sin^-1(1/n)
Step 2: Substitute in known values and calculate the critical angle.
C = sin^-1(1/1.52) = 41.1°
If light strikes the internal surface of crown glass at above 41.1° then it will be totally internally reflected.
What are Optical Fibres and their uses
Optical fibres are designed to totally internally reflect pulses of visible light (or occasionally infrared) travelling through them. They have many uses, including transmitting data for fast broadband connections and images from inside patients during keyhole surgery.
How does a simple Optical Fibre work?
A simple optical fibre has a fine glass core surrounded by a glass cladding with a lower reflective index. Light travelling through the fibre is contained within the core because of total internal reflection at the core/boundary.
How can you determine the refractive index from the critical angle?
A simple experiment to determine the refractive index of a material can be carried out by carefully measuring the critical angle of a semi-circular block.
Directing the ray of light towards the centre of the semi-circular block ensures that light enters the block at 90° to the boundary and does not change direction, so the critical angle can be measured accurately.
