Waves

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What is the formula that links frequency and number of cycles?

Frequency = cycles/seconds

What are the 2 types of progressive waves?

Longitudinal and Transverse

How do particles oscillate in mechanical waves?

They oscillate about fixed points

Define a progressive wave ‘

An oscillation that transfers energy and information

Define a transverse wave

A wave in which the particles oscillate perpendicular to the direction of the wave travel and energy transfer

What type of progressive wave can be polarised?

• Transverse waves can be polarised.

• Longitudinal waves can’t be

Give 2 examples of transverse waves

• EM waves

• Vibrations on a guitar string

Define a longitudinal wave

A wave in which the particles oscillate parallel to the direction of the wave travel and energy transfer

Give 2 examples of longitudinal waves

• Sound waves

• Ultrasound waves

Define the displacement of a wave

The distance of a point on the wave from its equilibrium position

Define the amplitude of a wave

The maximum displacement of a particle in the wave from its equilibrium position

Define the wavelength of a wave

The distance between points on successive oscillations of the wave that are in phase

Define the time period

The time taken for one complete oscillation or cycle of the wave

Define the frequency of a wave

The number of complete oscillations or wavelengths passing a point per unit time

Define wave speed

The distance travelled by the wave per unit time

Define phase difference

How far the cycle of one point is compared to another point on the same wave

How can the phase difference be found?

• From the relative positive of the crests or troughs of two different waves of the same frequency

• When the crests or troughs are aligned, the waves are in phase

• When the crest of one wave aligns with the trough of another, they are in antiphase

What is the phase difference between 2 points in phase?

360 degrees / 2Pi radians

What is the phase difference between 2 points in anti-phase?

180 degrees/ Pi radians

What are the axis on an oscilloscope?

• The x-axis is the time-base 

• The y-axis is the voltage

What do progressive waves transfer?

Energy

Define the intensity

The amount of energy passing through a unit area per unit time

I=P/A

How are intensity and amplitude related?

Intensity is proportional to amplitude squared

How does intensity vary with distance from a point source of waves(spherical waves)?

Inverse square law

I = P / 4πr²

What is a spherical wave?

A wave from a point source which spreads out equally in all direction

What are peaks of a wave

The maximum positive displacements

What are troughs of a wave

The maximum negative displacements

What are compressions of longitudinal waves?

Areas of high pressure due to particles being close together.

What are rarefactions of longitudinal waves?

Areas of low pressure due to the particles spread further apart

State some properties of EM waves

• They are all transverse waves

• They can all travel in a vacuum

• They all travel at the same speed in a vacuum (free space)

• May be reflected / refracted / diffracted

• May be polarised

Put the following in order from highest to lowest frequency: X-rays, Radio, Microwaves, UV, Visible

• Highest: X-rays

• UV

• Visible

• Microwaves

• Lowest: Radio

State the range of wavelengths (in powers of 10) of radio waves

>10⁻¹

State the range of wavelengths (in powers of 10) of microwaves

10⁻¹ - 10⁻³

State the range of wavelengths (in powers of 10) of infrared

1x10⁻³ - 7x10⁻7

State the range of wavelengths of visible light

4x10⁻⁷ - 7x10⁻⁷

State the range of wavelengths (in powers of 10) of ultraviolet

4x10⁻⁷ - 1x10⁻⁸

State the range of wavelengths (in powers of 10) of X-rays

1x10⁻⁸ - 4x10⁻¹³

State the range of wavelengths (in powers of 10) of gamma rays

1x10⁻¹⁰ - 1×10^-16

What is the difference between mechanical waves and electromagnetic waves?

EM waves don't require a medium.

What is an electromagnetic wave?

An oscillation of the electric and magnetic fields at right angles to each other.

Do all electromagnetic waves have the same time period?

They all travel at the same speed - but their wavelengths, frequencies and time periods vary.

What is polarisation?

Its when particle oscillations occur in only one of direction perpendicular to the direction of wave propagation

What does it mean when transverse waves are polarised?

• Vibrations are restricted to one direction

• These vibrations are still perpendicular to the direction of energy transfer

Why can’t longitudinal waves be polarised?

Because they oscillate parallel to the direction of travel

What is the effect of a polarising filter?

It only transmits the component of the oscillations parallel to the filter

What is the effect of perpendicular polarising filters?

No light is transmitted

Give a use of polarising filters.

• LCD screens

• 3D TV

• Anti-glare sunglasses

What are ways to polarise light other than using a polarising filter?

WhLight can also be polarised through reflection, refraction and scattering

What can microwaves be polarised by?

A metal grille

How is a metal grille different from a polarising filter?

• The free electrons moving in the metal bar can cancel out the electric field in the same direction as the grille and completely absorb it

• Therefore the horizontal electric field passes if the grilles are positioned vertically and vice versa

• This is the opposite of what happens in a polarising filter

Describe how you can observe the polarisation of microwaves?

• Place a microwave receiver in front of the transmitter and rotate about the axis through them

• The signal, which is detected using an ammeter or audio amplifier and loudspeaker will rise and fall with intensity as the receiver is rotated

• When the transmitter and the polarisation axis of the receiver are perpendicular to each other, the signal will be 0

• When the receiver has a maximum signal, a metal grille can be placed between the transmitter and receiver

• This acts as a second polariser

• When the grille is rotated the signal varies and is 0 when the metal rods are aligned with the electric field vector of the emitted microwaves

What’s the effect of a metal bar grille being horizontally orientated?

• Very few of the microwaves will be absorbed

• The ammeter will read a high value

What’s the effect of a metal bar grille being vertically orientated?

• All of the microwaves will be absorbed because they are vertically plane-polarised

• The ammeter will read 0

What happens to light when it moves from less dense to a more dense material?

The light bends towards the normal

What happens to light when it moves from a more dense to a less dense material (refraction)?

The light bends away from the normal

What causes the change in direction of light when it moves from one substance to another?

• The change in direction occurs due to the change in speed when travelling in different substances

• When light passes into a denser substance the rays will slow down, hence they bend towards the normal

What properties of waves change during refraction?

• Speed

• Wavelength

What property of the wave doesn’t change during refraction?

Frequency

What is a material with a high refractive index called?

Optically dense

What is snells law?

n₁ sin θ₁ = n₂ sin θ₂

• n₁ = the refractive index of material 1

• n₂ = the refractive index of material 2

• θ₁ = the angle of incidence of the ray in material 1

• θ₂ = the angle of refraction of the ray in material 2

Where is the angle of incidence and refraction taken from?

Its always taken from the normal

Describe the experiment to investigate the refractive index of a block

1. Place the semi-circular block on top of the protractor with the centre of its diameter aligned with 0° on the protractor

2. Direct the light from the lightbox towards this 0° and draw a dotted line perpendicular to the long edge of the semi-circular block. This is the normal

3. Using the pencil and ruler, trace the ray entering the block and leaving

4. Repeat this, moving the ray around every 10° up to 80. This is the angle of incidence, θ₁

5. The angle of the ray leaving the block from the normal is the angle of refraction, θ₂.

6. Record the angle at which the angle of refraction is 90°, (the ray leaves along the straight boundary of the block) just before it is reflected.

7. This is the critical angle

8. Repeat the experiment for the rectangular glass block

9. Use SinC=1/n

What is the angle of refraction at the critical angle?

90 degrees

What is the critical angle?

When the angle of refraction is exactly 90° so the light is refracted along the boundary

When does total internal reflection occur?

• When the angle of incidence is greater than the critical angle

• When the incident refractive index n₁ is greater than the refractive index of the material at the boundary (n₂₎

What are the conditions required for total internal reflection?

• The angle of incidence, θ₁ > the critical angle, C

• Wave must meet a boundary with a material of lower refractive index.

What are some wave phenomena’s?

• Reflection

• Refraction

• Polarisation

• Diffraction

What is the key feature of reflection?

The angle of incidence i is equal to the angle of reflection r

Define refraction

When light travels at a different speed when travelling through another medium

What is polarisation?

Its when the vibrations of transverse waves are restricted in one direction

Define diffraction

The spreading out of waves after passing through a slit/around an obstacle.

What is the only property of a wave that changes when it diffracts?

Its amplitude

When are the effects of diffraction most prominent ?

When the gap size is approximately the same or smaller than the wavelength of the wave

What happens as gap size increases during diffraction?

The effects gradually gets less

What can the diffraction pattern of light be represents as?

A series of light and dark fringes which show the areas of maximum and minimum intensity

What is the principle of superposition of waves?

When two or more waves with the same frequency arrived at a point, the resultant displacement is the sum of the displacements of each wave

Describe a superposition experiment using sound

• If two loudspeakers are connected to the same signal generator, the superposition of the sound waves can be heard when walking along in front of the speakers

• A loud sound is heard when the sound waves reinforce one another

• A quiet or no sound is heard when the waves cancel each other out

Describe a superposition experiment using light

• The superposition of light waves is demonstrated through:

  • Young's double-slit experiment

  • Diffraction grating

• The light waves are superposed when they reach a screen

• Monochromatic laser light is commonly used for these experiment to produce the clearest interference pattern on the screen

• The distance between the maxima and minima on the pattern varies with the frequency of the light (colour)

Describe young’s double slit experiment

1. Set up the apparatus by fixing the laser and the slits to a retort stand and place the screen so that D is 0.5 m, measured using the metre ruler

2. Darken the room and turn on the laser

3. Measure from the central fringe across many fringes using the vernier callipers and divide by the number of fringe widths to find the fringe width, w

4. Increase the distance D by 0.1 m and repeat the procedure, increasing it by 0.1 m each time up to around 1.5 m

5. Repeat the experiment twice more and calculate and record the mean fringe width w for each distance D

What is Young's double-slit experiment?

• A single source of light directed towards a double slit, which creates two coherent beams of light.

• This interferes as it hits the screen and creates an interference pattern.

What occurs to cause a dark fringe in the double slit experiment?

Destructive interference of the light from each slit

What occurs to cause a bright fringe in the double slit experiment?

Constructive interference of the light from each slit

What is constructive interference?

When two waves superpose in phase causing an increase amplitude.

What is destructive interference?

When two waves superpose in antiphase causing a decreased amplitude.

What is an interference pattern?

A pattern of regions of constructive and destructive interference produced by coherent sources of waves.

When does interference occur?

When waves overlap and their resultant displacement is the sum of the displacement of each wave

What type of waves does the principle of superposition apply to?

All types of waves

What term describes a phase difference of zero between two points on a wave?

In phase

If two waves are in phase will they constructively or destructively interfere?

Constructively

What path difference is required for waves to be in phase?

A whole number of wavelengths

What term describes a phase difference of pi radians between two points on a wave?

In antiphase

What path difference is required for waves to be in antiphase?

An odd number of half wavelengths

What term describes a phase difference of π radians between two waves?

In antiphase

What must waves have to be coherent?

• The same frequency

• A constant phase difference

Define path difference

The difference in distance travelled by two waves from their sources to the point where they meet

Define phase difference

The difference in phase between two waves that arrive at the same point

Describe how you can use sound waves to demonstrate 2 source interference

• Sound waves are longitudinal waves so are made up of compressions and rarefactions

• Constructive interference occurs when two compressions or two rarefactions line up and the sound appears louder

• Destructive interference occurs when a compression lines up with a rarefaction and vice versa. The sound is quieter

Describe how you can use Microwaves to demonstrate 2 source interference

• Two source interference for microwaves can be detected with a moveable microwave detector

• Constructive interference occurs in regions where the detector picks up a maximum amplitude of the signal

• Destructive interference occurs in regions where the detector picks up no signal

What must the sources of the wave be for 2 source interference to be observed?

• Coherent (constant phase difference)

• Monochromatic (single wavelength)

When can you use the double slit equation

when a << D