Waves & Energy Transfer

Physics 11

Introduction to Waves

Chapter 11 (§11-1, 11-7, 11-8)

Waves are all about Periodic Motion.

Periodic motion is motion that repeats after a certain period of time.This time is appropriately known as the

“period”, T.

Time

CrestTrough

Frequency

This is the number of oscillations per second.It is related to the Period

Frequency is measured in Hertz (Hz)

If you hear “Hertz”, think “per second”

PeriodFrequency

1 T

f1

sHz 11515

Quick Example

A pendulum has a period of 0.25s, what is it’s frequency?

“4Hz” so think “4 per second”

This makes sense, because if it takes ¼ of a second to make one oscillation, it will do 4 in one second.

HzssT

f 41

25.0

1

25.0

11

Common places to use Frequency

Computer processors“the Pentium 4 operates at 3.8 GHz”

(calculations per second)

Digital music and video“The audio file was encoded at 128 kHz”

Heart rate“his heart rate was 80bpm”

Beats per minute (1/time)

Amplitude

The “Amplitude”, A, of a wave describes how much the wave deviates from it’s equilibrium/average position (math class, the sinusoidal axis)

Time

Types of Waves

Sound Waves-a longitudinal wave

Light (EM) Waves

Mechanical Waves

So far we have only dealt with things that oscillate in time.

Waves can exist in substances tooDisturbances of this sort are referred to as

‘Mechanical Waves’ Water wavesSound wavesWaves in springs

You may be wondering about Light..

Light is a wave too, but it doesn’t travel though any “stuff” Originally they thought it must go through

something, and they called this stuff ‘ether’They looked for evidence of this ether, but were

unable to find evidence of it.Michelson-Morley Experiment

Not ‘mechanical’ in the sense the other disturbances are.

has many of the same properties

Electromagnetic (EM) Waves (§ 22-5, 24-4)

Those that consist of oscillating electric and magnetic fields that move at the speed of light or “c” through space

Examples: visible light, radio and x-raysDo not require a medium for transmission

Electromagnetic (EM) WavesFrequencies of EM waves are displayed on the EM

spectrum:

• visible light of different wavelengths perceived as colors (R-O-Y-G-B-I-V)

Electromagnetic (EM) Waves

• Individual wavelengths can be observed using a diffraction grating

Electromagnetic (EM) Waves

Matter Waves

Wave-like behavior of particles, such as electrons

Use quantum mechanics to describe it

Electron diffraction pattern

Properties of Waves

Period T, still existsThe period is how long it takes a for one spot

along the wave to see a crest after it saw the last one

Frequency, f, still defined the same wayWavelength, λ, a new quantity.

Distance from crest to crest (or trough to trough)

λ,

T

Do waves move?

There is nothing physical that moves from one point to another

The disturbance does travelThe Universal Wave Equation:

fv λ,

T

Practice Questions

1. A metronome beats 54 times over a 55 s time interval. Determine the frequency and period of its motion.

2. A child swings back and forth on a swing 12 times in 30.0 s. Determine the frequency and period of the swinging.

Practice Questions

3. The speed of sound in air at room temperature is 343 m/s. The sound wave produced by striking middle C on a piano has a frequency of 256 Hz.

a. Calculate the wavelength of this sound.

b. Calculate the wavelength for the sound produced by high C, one octave higher than middle C, with a frequency of 512 Hz.

Practice Questions

4. Interstellar (a.k.a. “between the stars”) hydrogen gas emits radio waves with a wavelength of 21 cm. Given that radio waves travel at 3.0 x 108 m/s, what is the frequency of this interstellar source of radiation?

Reflection and Transmission

Chapter 11 (§ 11-11)

Waves at BoundariesWhen a wave moves from one medium to

another, its frequency remains the same but the speed changes

As the speed is related to the properties of the medium, the behaviour will depend on the media involved

The behaviour at the boundary will depend on whether the wave is travelling from a less dense medium to a more dense medium or vice versa

Waves at Boundariesan incident wave reaches a boundary between 2 media part of incident wave continues on in new medium with

same frequency transmitted wave part of wave moves backward from boundary in old

medium reflected wave if difference in media is small, amplitude of transmitted

wave will be almost as big as incident wave & amplitude of reflected wave will be relatively small (most of energy transmitted)

if 2 media densities are very different, most of energy will be reflected

Less Dense to More Dense Boundary

Whenever wave passes from less dense to more dense medium, reflected wave is inverted

More Dense to Less Dense Boundary

Whenever wave passes from more dense to less dense medium, reflected wave is erect, not inverted

Video 1Video 2

Wave Interference

Chapter 11 (§ 11-11, 11-12)

Wave Superposition

Principle of Superposition states:

"the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by

individual waves" result of superposition is interference

Wave Superposition

Constructive interference occurs when amplitudes are in same direction

result is wave with larger amplitude than any individual wave

Wave Superposition

Destructive interference occurs when amplitudes are in opposite direction

as 2 pulses overlap, displacement is reduced

Standing Waves

waves are able to pass through one another unchanged 2 pulses with equal but opposite displacements meet

(destructive interference) find one point that is undisturbed node

2 pulses with equal displacements in the same direction meet (constructive interference) find point of maximum amplitude antinode

wave in which nodes and antinodes are stationary standing wave

Fixed Both Ends

Nodes at either end1st harmonic is half a

wavelength, with an anti-node (maxima) in the middle

2nd harmonic is one wavelength with a node in the middle and maxima between nodes

Fixed One End (§ 12-5)

Generally “seen” in sound waves

1st harmonic is one quarter of a wavelength with a node and maxima

2nd harmonic is 3/4’s of a wavelength with two nodes and two maxima

Guitar String

A guitar string has a given (open) length, given tension (and therefore mostly constant wave speed in a string) and therefore, when a string is plucked, a specific frequency is heard

If the string is then shortened by a certain amount, a higher frequency can be played

Superposition and Spectra

Physics 11

Multiple waves

We now understand the very basics of waves but reality usually does not involve one just one wave.Multiple radio stations transmitting into the roomWaves on the surface of a pool as people are

jumping inWhite light (it is a composite of waves in the EM

spectrum)

So what doe these waves look like?

Superposition

Superimpose two waves together.Add them together

For each value of x, add the value of each wave to get a resultant

Real Waves are Superpositions

This means that real waves have a number of waves adding together to make them up.Each part having a different wavelength

The wavelengths that are used to construct a complex wave are referred to as a “Spectrum” (plural, ‘Spectra’)

Spectrum Graphs

Real waves are composed of many components

To keep track of what wavelengths are used, a simple chart is often made.

Consider the emission spectrum of Hydrogen

It tells us what wavelengths are present, indicating the wavelength qualitatively with the color of light

Hydrogen

How are spectra formed at the atomic level?

Intensity Spectra

Spectra plots can include information about amplitude at each wavelength

Consider these plots made for common ‘white light’ or WL sources

Various WL sources

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

350 400 450 500 550 600 650 700 750

Wavelength (nm)

Reli

tive i

nte

nsit

y (

arb

un

its)

solar 1

incandecent bulb

flouresent blub

lcd white

crt white

Wave Behaviour

Physics 11

Diffraction (§ 11-13, 24-6)

When a wave impinges on a single opening, it will diffract

That is, a plane wave will spread through space and the spreading angle is a function of wavelength and opening

Single Slit Diffraction

If light is impingent on a single slit, the light wave will spread

The spreading angle is related to the size of the opening and the wavelength of light used

Two Point Sources

Two point sources will also interfere to create an interference pattern

The interference pattern is based on wavelength and separation of point sources

Young’s Double-Slit Experiment (§ 24-3)

If light is impingent on two slits, the light will spread from each slit like in the single slit case

However, the waves will interfere with each other and an interference pattern will result

Diffraction Gratings

A diffraction grating combines the behaviour of a single slit and double slit and is created by creating many grooves or slits on a transparent or reflective material

Diffraction Grating

These examples of diffraction gratings have many grooves (or slits) and as a result, separates light into its constitute wavelengths (colours)

Doppler Effect (§ 12-8, 12-9)

When an source is moving with respect to an observer (or vice versa) the frequency of the sound will shift due to the Doppler Effect

As a result, it is possible to determine whether an object is moving toward or away from us if we know the reference frequency

Doppler Effect

Doppler Effect

For sound…As a sound source moves towards the observer or receiver, the frequency or pitch increasesAs the sound source moves away from the receiver, the frequency decreases

Sonic BoomA sonic boom is the sound associated with the shock

waves created by an object traveling through the air faster than the speed of sound.

Sonic booms generate enormous amounts of sound energy, sounding much like an explosion.

Ex: supersonic jets, cracking of a whip, “pop” of a balloon

For light…

We can see the same behaviour with light; since light (in a vacuum) must always travel at the speed of light (3.0x108 m/s)

However, since nothing can travel faster than the speed of light (in a vacuum) it is impossible to see behaviour akin to a sonic boom with light (in a vacuum)

Red and Blue Shift When the wavelength or frequency of light is changed, so is

its “colour” For visible light, this means that when an emitter is moving

away from Earth, the wavelength observed is increased and light is said to be red shifted

When light is emitter by a body moving toward Earth, wavelength is decreased and we say that it is blue shifted

Ex: rotation of galaxies; Hubble’s expansion of Universe

Cerenkov Radiation

Cerenkov radiation is EM radiation emitted when a charged particle (such as an electron) passes through a medium at a speed greater than the speed of light in that medium.

Ex: blue light from nuclear reactor

Reflection (§ 11-11, 23-2)

According to ray optics, reflection can be modelled using a ray impingent on a mirror at some angle and reflected at the same angle

θi = θr

Refraction (§ 11-13, 23-4, 23-5, 23-6) Refraction is the change in direction or bending of light at boundary

between 2 media Optically Dense - when speed of light in one medium is slower than that in

another when angle of incidence = 0o , angle of refraction = 0o speed changes but

passes straight through, along the normal when light travels into a medium where it travels faster, angle of refraction

> angle of incidence OR if light enters less optically dense medium, refracted rays bend away from the normal

if light enters more optically dense medium, refracted rays bend toward the normal

  Index of Refraction (n) - ratio of the speed of light in a vacuum to its speed

into a material

ss v

cn

Refraction

Light bends inward when entering medium   of higher index of refraction

Light bends outward when entering medium of lower index of refraction

Snell’s Law Light moving from smaller n to larger n is bent toward normal & vice-versa

ni is index of refraction for incident medium

nr is index of refraction for second medium are angles of incidence & refraction

refractive index (n) can be found by measuring angles of incidence & refraction

Critical Angle

Critical Angle (θc) occurs when the refracted ray lies along the boundary of the medium surface 

Total Internal Reflection Total Internal Reflection occurs when light passes from a more optically

dense medium to a less optically dense one at an angle so great that there is no refracted ray

Ex: fiber optic cable, internal body probe