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Waves• Content• 15.1 Progressive waves• 15.2 Transverse and longitudinal waves• 15.3 Polarisation• 15.4 Determination of speed, frequency and wavelength• 15.5 Electromagnetic spectrum• Learning Outcomes• (a) describe what is meant by wave motion as illustrated by vibration in

ropes, springs and ripple tanks.• (b) show an understanding and use the terms displacement, amplitude,

phase difference, period, frequency, wavelength and speed.• (c) deduce, from the definitions of speed, frequency and wavelength, the

equation ν = fλ.• (d) recall and use the equation ν = fλ.• (e) show an understanding that energy is transferred due to a progressive

wave.• (f) recall and use the relationship, intensity is proportional to (amplitude)2.

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• (g) compare transverse and longitudinal waves.• * (h) analyse and interpret graphical representations of transverse and

longitudinal waves.• (i) show an understanding that polarisation is a phenomenon associated

with transverse waves.• * (j) determine the frequency of sound using a calibrated c.r.o.• * (k) determine the wavelength of sound using stationary waves.• * (l) state that all electromagnetic waves travel with the same speed in free

space and recall the orders of magnitude of the wavelengths of the principal radiations from radio waves to γ-rays.

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Waves

• Waves are everywhere in nature.

• A wave is a disturbance that transfers energy between 2 points through vibrations in a medium, without transferring matter between the 2 points

• Waves which move energy from place to place are called progressive waves. Waves that do not are called stationary waves

• 2 most common types of waves - sound waves and light waves.

• For sound waves we think of the vibrating object as the medium

• For light waves we think of the vibrating objects as electrons or charged particles

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A wave transports energy and not matter

When a wave is present in a medium (that is, when there is a disturbance moving through a medium), the individual particles of the medium are only temporarily displaced from their rest position.

There is always a force acting upon the particles which restores them to their original position

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Behaviour and characteristics

In a slinky spring, a person does work by moving his hand and hence transferring kinetic energy to the first coil.

The first coil receives a large amount of energy which it subsequently transfers to the second coil.

When the first coil returns to its original position, it possesses the same amount of energy as it had before it was displaced. The first coil transferred its energy to the second coil.

The second coil then has a large amount of energy which it subsequently transfers to the third coil.

In this manner, energy is transported from one end of the slinky to the other, from its source to another location

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Categories of Waves

Waves come in many shapes and forms One way to categorize waves is on the basis of the direction of movement of

the individual particles of the medium relative to the direction in which the waves travel.

Categorizing waves on this basis leads to two notable categories: transverse waves and longitudinal waves.

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Transverse waves

A transverse wave is a wave in which the vibrations of the particles of the wave are at right angles to the direction in which the energy of the wave is travelling

Examples: water waves, electromagnetic waves, seismic waves

Seismic waves are made up of P(primary) waves which are longitudinal and S(secondary) waves which are transverse

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Longitudinal waves

A longitudinal wave is one in which the direction of the vibrations of the particles in the wave is along the direction in which the energy of the wave is travelling.

Example: a sound wave which vibrates forwards and backwards

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longitudinal waves cont…

Compression - maximum density Rarefaction - minimum density

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Electromagnetic vs Mechanical Waves

Another way to categorize waves is on the basis of their ability or inability to transmit energy through a vacuum (i.e. empty space).

Categorizing waves on this basis leads to two notable categories: electromagnetic waves and mechanical waves.

An electromagnetic wave is a wave which is capable of transmitting its energy through a vacuum.

Electromagnetic waves are produced by the vibration of charged particles A mechanical wave is a wave which is not capable of transmitting its

energy through a vacuum.

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Anatomy of a wave

The peak or crest/compression of a wave is the point on the medium which exhibits the maximum amount of positive or upwards displacement from the rest position. i.e. points A, E and H

The trough/rarefaction of a wave is the point on the medium which exhibits the maximum amount of negative or downwards displacement from the rest position i.e. points C and J

Wavelength, λ, is the distance between 2 successive crests or troughs, e.g. A-E or E-H or ½ C-J

A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude.

Putting a lot of energy into a transverse pulse will not affect the wavelength, the frequency or the speed of the pulse.

The energy imparted to a pulse will only effect the amplitude of that pulse.

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Wave formula or simple harmonic motion (shm)

Displacement of a particle on a wave is its distance from its rest position Simple harmonic motion (SHM) is a displacement that varies cyclically and

is mathematically described asx(t) = A sin (2πft + Φ) where 2πf = ω A is amplitude, defined as the maximum displacement f is frequency Φ is phase angle (fraction of a complete cycle corresponding to

an offset in the displacement) • All waves, whether transverse or longitudinal, exhibit shm

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Related definitions & terms

• The period (T) is the time in seconds it takes to go through one complete cycle, or oscillation, or wave cycle. Since v = 2πr/T, T = 2πr/v or T = 2π/ω since v = r ω

• The frequency (f) is the number of complete cycles an oscillating object makes in one second i.e. f = 1/T is in Hz

• The angular frequency (ω) is the change in angle per unit time i.e. ω = 2π/T and ω = 2πf.

• The phase difference is the difference in step of vibration for two points along the oscillating path– when the crests and troughs of 2 waves of the same frequency are aligned,

they are in-phase (i.e. 0°)– when a crest is aligned with a trough, the waves are out-of-phase (i.e. 180°)

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Intensity

• Since waves carry energy, the amount of energy passing through unit area per unit time is called the intensity I of the wave

• The energy transported by a wave is directly proportional to the square of the amplitude of the wave, i.e E = kA2

• The intensity of a wave I is directly proportional to the square of its frequency f , I = kf2

• For a wave of amplitude A and frequency f, the intensity I is proportional to A2f2

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The wave equation and principle

Speed = distance/time Wavelength is the distance moved by the wave in one cycle i.e distance Time = period = 1/frequency So speed = wavelength/period

Speed = wavelength x frequency, i.e v = f λ The principle is that wave speed is dependent upon medium properties and

independent of wave properties.

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Properties of wave motions

All waves exhibit reflection, refraction and diffraction at boundaries from one medium to another associated with the bending of the path of a wave and can produce interference patterns

Reflection involves a change in direction of waves when they bounce off a plane barrier i.e. angle of incidence equals the angle of reflection. No change in wavelength but direction. If curved mirrors are used, waves can converge or diverge

Refraction of waves involves a change in the direction of waves due to a change in speed as they pass from one medium to another. Frequency does not change hence wavelength changes

Diffraction involves a change in direction and spreading of the waves as they pass through a narrow gap, an opening or around a barrier/obstacle in their path

Interference is when 2 or more waves overlap, and their resultant displacement is the algebraic sum of the individual components

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Example

A wave of frequency 400 Hz is traveling at a speed of 320 m/s. Calculate the phase difference between two points 0.2 m apart on the wave.

Solution

v 320wavelength, = 0.8m

f 400

Phase difference of 0.2m apart

0.2 0.2 1= (2 ) (2 ) rad

0.8 2

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Related example• Submarines can now transmit and receive e-mails, without having to

surface.

An 'accoustic modem' on the submarine transmits sound waves through water, at a frequency of 8.0 kHz. The waves carry information at 2.4 kbit s-1 to a radio buoy. The information is relayed from the buoy to shore by radio waves. The buoy can also receive radio signals, and transmit the information as sound waves back to the submarine.

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a) Show that the wavelength of the 8.0 kHz sound waves in sea water is about 0.2 m given that the speed of sound in sea water is 1500 m s-1

Solution

λ = v/f = 1500/8000 = 0.19 m ~ .2 m

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b) The sound waves travel 5.0 km from the submarine to the buoy.

Calculate the time taken for the sound waves to travel this distance.

5000

1500 =3.3s

st

v

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Polarization

• Process by which a wave’s oscillations are made to occur in one plane only

• Associated with transverse waves only• Longitudinal waves cannot be polarized• Discovery of polarization around 1800, showed that light is a

transverse wave and opened the way for Maxwell’s theory of light as electromagnetic radiation

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Polariser/Polaroid sheet

• A polaroid sheet contains long chains of organic molecules aligned parallel to each other

• When unpolarised light arrives at the sheet, the component of the electric field of the incident radiation which is parallel to the molecules is strongly absorbed whereas radiation with its electric field perpendicular to the organic molecules is transmitted through

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Applications of polarisation

• Sunglasses – reduction of the glare of the reflected light allows one to see objects more clearly

• Stress analysis patterns in materials to avoid early failures through re-design

• Improved TV reception through selective polarised transmission to avoid interference between incident and re-transmitted signal

• Fishermen see fish more clearly

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Properties of electromagnetic waves

In vacuum, all electromagnetic waves travel at the same speed which is the speed of light 3.0 x 108 m/s

They are all transverse waves, with the oscillations being electric and magnetic fields. Like all waves, they can be reflected, refracted, diffracted and can interfere

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Gamma waves

These are the most dangerous and penetrating form of electro-magnetic waves. They have the shortest wavelengths, and highest frequency.

Gamma rays are emitted by some radioactive nuclei, and are also produced during supernova explosions. They do not need an electrical power source to be generated like X-rays

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X-rays

X-rays are produced from electrons stopped rapidly in a X-ray tube which needs an electrical power sourceX-Rays have high energy and such short wavelength that they can go right through us. However, they cannot get through bone as easily as they can get through muscle. Medical practitioners use them to look at our bones and our dentists to look at our teeth. Produced when high velocity electrons strike a metal target.

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Ultraviolet Radiation (UV)

A dangerous type of radiation.

Produced from very hot objects when electrons jump from relatively high excited states to low excited states or ground state within atoms and molecules

Emitted from the sun

UV is partly absorbed by the ozone layer

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Visible light

Produced also from very hot objects by atoms and molecules when the outer electrons, after being excited into higher energy levels, return to their unexcited state.

Made up of monochromatic light with different wavelengths.

Longest wavelength light we can see is red – 700 nm

Shortest wavelength light we can see is violet – 400 nm

Green is at 555 nm

Used for communications

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Infrared Radiation

• Produced from hot objects and generated by vibration and rotation of atoms & molecules.

• Detectable by our skin as heat radiation

• Keeps the earth warm

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Microwaves

• Are produced from electrons oscillating in magnetrons

• Very short wavelength.

• Used in radar, communications, broadcasting and preparation of food.

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Radio wavesProduced from electrons oscillating in aerials

Longest of all the electromagnetic waves

Used in telecommunications (radio and TV broadcasts, as well as mobile phones and walkie talkies).

2 common ways to transmit radio waves

a) Amplitude modulation (AM)

b) Frequency modulation (FM)

Some radio waves come through the earth's atmosphere from space