Waves

Waves are Energy

Kinds of waves

• Mechanical waves

• Electromagnetic waves

• Matter waves?

What is a wave?

• A wave is a form of energy transfer:

– often through a disturbance in the

medium

– Same sine wave as you get with a

pendulum

Properties of

waves

• Amplitude

• Wavelength

• Frequency

• Period

• Medium?

• Direction

Inverse

• Ex 1: find the period of a wave with a

frequency of 0.25 Hz

Tf

1

fT

1

• Ex 2: find the frequency of a wave with

a period of 5 ms

ssHzf

T 425.0

1

25.0

111

HzsT

f 200005.0

11

• Ex 1: find the angular velocity of an object

with a frequency of 0.25 Hz

• Ex 2: find the angular velocity of an object

with a period of 5 ms

ω=2πf =2π(0.25Hz)

ω= 1.57 rad s⁻1

ω=2π/T =2π/0.005s

ω=1260rad s⁻1

Start p. 103 #1-2

Pendulum Lab • Name

• Date

• Block

• Partner Purpose: to measure g

Procedure: refer to text, p. 5 but with the following changes: …

Observations:

Lab Prep

Length /m Time (10) /s Period /s Period^2

0.10

0.15

0.20

0.25

0.30

0.35

• What does the graph tell us?

• Since g

lT 2

slopeT

lg

2

2

2 44

• Find g from your graph, then write a conclusion comparing your result to gravitational field g=9.8 m/s2

Simple Harmonic Motion

• Ex 3: sketch the graph of motion of the object from

example 1 if it started from 7cm above equilibrium position

x=7cos(1.5t)

Start p. 105 #3-6

• Ex 4: find the velocity at 2.7s

v= -ωxosin(ωt)

v=-11sin(1.57t)

v=9.8cm s⁻ⁱ

Simple harmonic motion

We have angular velocity: ω=2πf and ω=2π/T

This gives:

Ex 5: find the velocity at 2.7 cm

v= 1.57 sqrt(7^2-2.7^2)

v=10.1cm s⁻1

Start p. 107 #7-9

Variable Symbol Unit

Amplitude x0 m

Period T s

Frequency f Hz

Angular frequency

AKA angular velocity

s-1

Displacement (relative

to equilibrium)

x m

Force F N

Time t s

We can “hear” wavelength as pitch

How does our ear pick up these frequencies?

Some snakes can see infrared light

Bees can see in UV

• The mantis shrimp is a delightfully weird beastie. They’re multi-coloured, their genus and species names mean ‘mouth-feet’ and ‘genital-fingers’; they can move each eye independently, they see the world in 11 or 12 primary colours as opposed to our humble three, and now we find that this species can see a world invisible to the rest of us, said Professor White, of the University of Queensland.

• Mantis shrimps, dubbed “thumb splitters” by divers because of their vicious claws, have the most complex eyes in the animal kingdom, capable of seeing colors from the ultraviolet to the infrared, as well as detecting other subtle variations in light.

• They view the world in up to 12 primary colors- four times as many as humans - and can measure six different kinds of light polarization, Swiss and Australian researchers reported.

How damp is it?

How damp is it?

An object undergoing SHM will lose amplitude due

to friction, fluid resistance, etc.

The amount of damping can be classified as:

Start p. 107 #7-9

Lab 8.2 p. 155 Gore Text

1. Waves were faster in the smaller slinky

2. Same

3. Amplitude does not affect wave speed

4. Spring tension is proportional to speed

5. Only the disturbance travels

6. The waves reflected inverted (crest

reflected as a trough)

The wave equation

• For a wave with speed v, frequency f and

wavelength , we have:

v=f Ex 1: find the speed of a water wave with

wavelength 2.5 m and frequency 3 Hz

Don’t forget:

• Chocolate Lab: use a (pure) chocolate bar,

the bigger the better, and a microwave oven

to measure the speed of light

• Bring the chocolate for a Wednesday lab

day.

Wave transmission

• When a wave encounters a different

medium, we always find:

– part of the wave is transmitted

– part of the wave is reflected

• The reflected wave will be:

– upright if the 2nd medium is less dense

– inverted if the 2nd medium is more dense

We can “see” wavelength as color

EM radiation

• For light, we have:

c=f Ex 1: find the frequency of green light

cf

m

sm

9

8

10550

100.3

Hz14105.5

Ex 2: find the speed of light if wavelength is

measured to be 14 cm

fc )102450(14.0 6

18104.3 sm

Ex 2: find the frequency of a 6.0 fm gamma

ray photon

cf

m

sm

15

8

100.6

100.3

Hz22100.5

• Ex 3: find the wavelength of “The River”

– f=97.5 MHz

– v=c

Hz

sm

6

8

105.97

1000.3

fcf

c

m08.3

Energy with SHM

Total energy is a constant, depending on amplitude x₀

By conservation of energy, this also means:

Kinetic energy

Ex: find the kinetic energy for a 10 g mass on a spring

stretched 13 cm, when it is at a position of -3.5 cm

Potential energy can be found from other information,

e.g. Gravity or solved from total energy

Ex: find the potential energy for a spring stretched 13 cm,

when it is at a position of -3.5 cm

• Lab 8-4 p.160 Tuesday?

• Exercises P.159 #1-6

Lab 8-4

p. 160-168

Do parts 1-4 Lab 8-4

Answer Concluding Questions:

#1-2 p. 161 (reflection from straight barrier)

#1-2 p. 162 (reflection from parabola)

#1-3 p. 163 (diffraction)

Wave “Action”

Types of wave “action”

• Refraction

• Diffraction

• Refl”action”?

Reflection

• We find the waves are reflected with the same angle

Diffraction

• We find the waves bend around the barrier

• We get more diffraction with long wavelength, small opening

Refraction

• We can bend waves when they encounter a different medium

Start p. 125 #10-12

What is resonance?

• If vibrations match an objects natural oscillation,

it resonates

• Greenhouse gases resonate in the infrared range

and absorb those frequencies

Interference

• When waves encounter each other, we have

found they pass through

• When they occupy the same location in

space, they interfere

• The resultant wave is the integer sum of the

individual waves at each point

Wave Interference

• Draw the resultant of these two waves

interfering. The resultant at each point is

the integer sum of the magnitudes.

• Draw the resultant of these two waves

interfering. Remember that the resultant

at each point is the integer sum of the

magnitudes.

• Constructive vs.

destructive

interference

Start p. 127 #13

The Doppler Effect

Stationary Source

• Since the waves

move outward in

concentric spheres,

the wavelength is

observed as being

equal in all

directions.

Moving Source

• These circles no longer

have the same centre.

• The observer will

measure a different

wavelength from a

different direction

Light Doppler?

• Very fast moving objects will even show a

Doppler effect with emitted light

• Blue shift: moving towards us

• Red shift: moving away

• This is how we know the universe is

expanding!

Doppler formula

• If the source is moving:

• Ex: find the frequency we hear for a 3000Hz sound from a car moving towards us at 25 m/s

• Ex: find the frequency we hear for a 3.0 kHz sound from a car moving towards us at 25 m/s

25330

3303000f

Hzf 3200

Doppler formula

• If the observer is moving:

• Ex: find the frequency we hear for a 250Hz sound if we run away at 13 m/s

Ex: find the frequency we hear for a 250Hz sound if we run away at 13

m/s

330

13330250f

Hzf 240

Doppler formula

• For light:

• Ex: find the change in frequency we see for red light if a star moves away at 513,000 m/s

cf

f

fc

c

ff

9

8

10700

103

cf Hz141029.4

8

14

103

513000102857.4

Hz11103.7

P. 136 q’s 17-19

P. 138 q’s 20-22

Snell labs due Monday

Shock Waves?

• As the source moves faster through the medium, you can

see that the wavefronts start piling up in front of the

object, e.g. the “sound barrier.”

• Approaching the speed of sound the craft encounters the

sound waves piled on top of each other.

• Once the craft breaches the “sound barrier,” it leaves its

sound waves behind.

• The edges of these waves form a shock wave known as

the “sonic boom”

P. 201 Test Yourself 1-11 odds

Labs due now

Scattering

Speed of Light

“c”

Why is light so difficult to measure?

• Compared to sound (343 m/s) light seems

instantaneous

• Galileo made the first attempt to measure c

Why is light so difficult to measure?

• Roemer (1676) made

the first successful

measurement, from

eclipses of Io

~200 000 km/s

More accurate measurements

• Bradley (1728)

– stellar aberration (301 000 km/s)

• Fizeau

– rotating wheel (313 000 km/s)

• Foucault

– rotating mirror (299 796 km/s)

• Michelson-Morley interferometer

– 299 792.458 km/s

Measure the æther wind?

• Since all waves need a medium, it was

believed light moved through a medium

called the æther.

• The Michelson-Morley interferometer was

precise enough to measure the æther wind

rushing past the Earth

• Results?

• They measured the same speed!