Waves

Waves

What is a progressive wave

A wave that transfers energy

A mechanical wave

Mechanical waves are waves that require a medium in order to transfer energy away from their source through the oscillation of particles. Some common examples of mechanical waves are earthquake waves that travel through layers within the earth. Sound waves are also mechanical waves that travel through the air, water, and solid matter.

Define a longitudinal wave

A wave where the particles oscillate parallel to the direction of energy transfer

State examples of longitudinal waves

Sound

Ultrasound

Define a transverse wave

A wave where the particles oscillate perpendicular to the direction of energy transfer

State examples of transverse waves

Electromagnetic waves

Surface water waves

Define displacement of a wave

Distance in a given direction moved by a particle on a wave relative to the equilibrium

Define amplitude of a wave

The maximum displacement from the equilibrium position

Define wavelength of a wave

The distance from one peak to the next consecutive peak.

The closest distance between two points which are in phase.

Define period of a wave

The time taken for a complete oscillation

Define phases difference

How far one wave / particle lags behind another wave / particle

Define frequency

The number of oscillations per unit time (DO NOT SAY TIME PERIOD)

State an equation linking time period and frequency

T = 1/f

Define speed of a wave

The distance travelled per unit time of the energy transfer

State the equation linking speed, v, wavelength and frequency of a wave

Speed = frequency x wavelength

v = f λ

Explain v = frequency x wavelength using definitions

If f waves are produced per second each of length - lambda. The distance travelled by the first wave in one second is f x lambda

Define reflection

Where the incident angle is the same as the reflected angle and the incident wave, normal and reflected wave all lie in the same plane

Explain refraction

The bending of light as it moves from one medium to another of different density due to the change in speed of the wave. Note: as the wave move from less dense to dense it bends in towards the normal

Define refractive index

The speed of light in a vacuum / speed of light in the medium

State snells law

n1sin x1 = n2sin x2

n1: the refractive index of medium 1 n2: refrcative index of medium 2 x1: the incident angle (w.r.t to the normal) x2: the refracted angle (w.r.t to the normal)

The critical angle

The angle of incidence that produces an angle of refraction of 90 degrees. Beyond the critical angle total internal reflection will occur.

State the two requirements needed for total internal reflection

One must be travelling from a dense to less dense medium. The angle of incidence must be larger than the critical angle.

The formula to determine the critical angle

n1 sin C = n2 sin 90

n1 sinC = n2 since sin90 = 1

State two problems associated with the transmission of data in fiber optic cables

Material and modal dispersion Loss of data via scratches / impurities along the optic fiber

Material dispersion

Different wavelength travel at different speed in a fiber optic and hence take different times to travel a set distance

How to reduce / illiminate Material dispersion

Use monochromatic light Use signal boosters at set distances Use graded index optic fibers

Modal dispersion

A wave can take a number of possible paths down the fiber optic and hence take different times to travel a set distance.

How to reduce Modal dispersion

Use thinner fibers to reduce the number of possible paths

If the refractive index of the core is close to that of the cladding a large critical angle is produced. This will reduce the number of possible paths available by the rays

What must you check and double check when you are given a refraction question involving the transmission of light from one medium to another.

The angles are with respect to the normal. If the angle is given with respect to the plane boundary you must remember to do 90 minus this value to obtain the angle with respect to the normal.

Define diffraction

The spreading of a wave as it passes a gap or edge. Maximum Diffraction occurs when the gap size is comparable to the gap size.

State the formula used to determine the angle of diffraction of the first minima through a single slit

Angle to first minima = wavelength / gap size

How could you increase the spreading of light through a single slit

1. Increase the wavelength (red spreads more than blue)

2. Decrease the gap size

State the formula used when you have two wave sources / one wave source and two slits

wavelength = (dist between slits x fringe seperation) / dist from slits to screen

• wavelength = s w / D

How could you increase the distance between fringes in young's slits? (This would reduce percentage uncertainty in measurement)

Increase the wavelength / decrease the frequency Increase the distance between slits and screen. Decrease the distance between the slits.

Explain the nature of electromagnetic waves

Waves which consist of an oscillating electric and magnetic field vectors - perpendicular to each other. Travel at 3 x 10^8 ms^-1 in a vacuum.

The wavelength of radio waves

~10^3m

The wavelength of micro waves

~10^-2m

The wavelength of infra red waves

~10^-5m

The wavelength of visible waves

400 nm - 700 nm

The wavelength of x - rays

~10 ^ -10m

The wavelength of Gamma rays

~10^-13 m

Something common to only electro magnetic waves

They all travel at 3 x 10^8 m/s in a VACUUM

They consist of oscillating electric and magnetic field vectors travelling perpendicular to each other

Similarities between all parts of the E - M spectrum

• They all travel at 3 x 10^8 m/s in a VACUUM

• They are all transverse waves

• They can all be polarised

• They all transfer energy NOT matter

• They are all produced via oscillating charges

Differences between all parts of the E - M spectrum

• They all have different frequencies, wavelengths and energies

• they all need a different gap size for maximum diffraction

• They are all produced and interact with matter differently

State a practical use of radio waves

Communication

State a practical use of micro waves

Communication, use in a microwave oven (resonance of water)

State a practical use of infra red

• thermal imaging

• use in remote controls

State a practical use of visible light

• sight

• photography

• Use in fibre optics

• lasers

State a practical use of U V

• Sterilisation

• Bar codes / security codes

State a practical use of X - Rays

• Medical imaging / CT scans

• Airport security

State a practical use of Gamma

• sterilisation of medical equipment

• Medical imaging

• Cancer treatment

Define what is meant by un - polarised light

A particle oscillates in an infinite number of planes - perpendicular to the energy transfer.

Define what is meant by polarised light

A particle oscillates in one planes - perpendicular to the energy transfer.

Better as….

You are limiting the displacement vector to a single plane

What type of wave can be polarised

Transverse waves NOT longitudinal waves

What type of wave is polarised in nature

Reflected light from a non metallic surface (eg water)

Why do TV aerials need to be rotated in order to improve the signal

The signals are polarized. The aerial will receive the maximum intensity when the plane of the polarized radio wave is the same as the plane of the aerial.

Define the principle of superposition

The resultant displacement is equal to the sum of individual displacements at the point the waves meet

Define interference

Where two waves meet they superpose

Define Coherence

Where there is a constant phase relationship between the two sources. The two sources have the same frequency

Define path difference

The difference in the distance travelled from two sources to a point

Describe constructive interference

Where waves superpose to give the maximum possible amplitude. Here the waves are in phase (0 radians) and have a path difference equal to a multiple of a wavelength

Describe destructive interference

Where waves superpose to give the minimum possible displacement. Here the waves are out of phase by pi radians and have a path difference equal to a multiple of half a wavelength.

Define Intensity

The power per unit cross sectional area

Intensity of a laser

I = Power of laser / area of circle

Intensity from a point source

I = power / area of a sphere

This is in the data sheet

State the diffraction grating formula

n λ= d sin θ d:

distance between successive slits θ: angle between central line and nth maxima λ: wavelength

What are the advantages of using multiple slits over young's slits to determine the wavelength of a light source

Multiple slits produce clearer maxima which are more spread which reduces percentage uncertainties in measurement

If there are 100 lines per mm how would one determine the distance between two consecutive slits, d

1 x 10^-3 / 100

If there are 100 000 lines per m how would one determine the distance between two consecutive slits, d

1 / 100 000

How would you determine the maximum number of fringes seen in a diffraction grating experiment if mono chromatic light is used ?

You would determine n using n λ= d sin θ by using θ = 90 degrees. You would then round this number down to a whole number. Multiply this by 2 (to include max on other side) and add one (to include central max)

How would you determine the maximum number of red fringes seen in a diffraction grating experiment if white light is used ?

You would determine n using n λ= d sin θ by using θ = 90 degrees. You would then round this number down to a whole number. Multiply this by 2 (to include max on other side) - this time the central maxima is white so don’t add this on here

How is a standing wave formed

An incident and reflected wave superpose to produce points of zero AMPLITUDE called nodes and points of maximum AMPLITUDE called anti - nodes.

State similarities between progressive and standing waves

They can both be longitudinal or transverse.

State differences between progressive and standing waves

Neighbouring points on a progressive waves have the same amplitude but stationary waves don't.
Neighbouring points on a progressive wave are out of phase but are in phase in a stationary wave.
A stationary waves stores pockets of energy. A progressive wave transfers energy.

What is the distance between neighbouring nodes or anti nodes on a standing wave

Half a wavelength

What is the length of closed pipe when one hears the first loud sound (node to anti node)

A quarter of a wavelength

Closed end: node

Open end: anti node

What is the length of an open pipe when one hears the first loud sound (anti node to anti node)

Half a wavelength

Both open end give anti nodes

What do we mean by first fundamental / 1st harmonic

A standing wave which goes from node to node only

State the formula which governs the frequency of the 1st harmonic on a string

f = (1/ 2 x length) x root (T/mass per unit length)

Where mass per unit length = area x density

Can you prove the above?