WAVES & ENERGY TRANSFER

“The impetus is much quicker than the water, for it often happens that the wave flees the place of its creation, while the water does not …”

Leonardo de Vinci

WAVES PROPERTIES

1. Transverse Waves:

The particles of the medium vibrate perpendicularly to the direction of the wave

Wave: Transfers energy without transferring matter

Types of waves:

wavelength

WAVES & ENERGY TRANSFER

2. Longitudinal Waves:

The particles of the medium move parallel to the direction of the wave

WAVES & ENERGY TRANSFER

3. Surface Waves:

A mixture of transverse and longitudinal wave properties

Parts of a Wave: Terminology

Wave, pulse, amplitude, crest, trough, wavelength, period, frequency, in phase & out of phase

WAVES & ENERGY TRANSFER

Wave

Pulse

WAVES & ENERGY TRANSFER

Frequency (f ):

Period (T):

The time to complete one cycle (a repeated event)

Measured in time units (sec., min. etc)

The number of cycles per time

Measured in Hertz (cycle/sec.) or in r.p.m (revolution per min.)

f = 1

TT =

1

fand

WAVES & ENERGY TRANSFER

Example 1.

A bicycle wheel makes 45 revolutions in 18 s. What is the period and frequency?

Solution: T = Time

# cycles=

18 s

45= 0.40 s

f = 1

T=

1

0.40= 2.5 Hz

WAVES & ENERGY TRANSFER

Playing with a Snakey Spring

Use the spring to answer the following questions:

1) What affects the speed of a wave?

3) What happens when two pulses travelling in opposites directions meet at one point in a spring?

2) Is the speed of a wave affected by the amplitude of a wave?

4) What travels faster along the spring, traverse waves or longitudinal waves? What does this tell you about P waves (first waves) and S waves (second waves) from an Earthquake?

WAVES & ENERGY TRANSFER

Results of Playing with a Snakes Spring

WAVES & ENERGY TRANSFER

Summing up the properties of waves so far:

• Wave transfer energy without transferring mass

• Three types of waves:

• Transverse

• Longitudinal

• Surface waves

• Wavelength, amplitude and pulse are important quantities in waves

• Frequency & Period are reciprocals of each other

• The speed of a wave is set by the medium

• Waves bounce off fixed-ends and free-ends differently

UNIVERSAL WAVE EQUATION

There is a relationship between the speed, wavelength, and frequency of a wave.

v = λ x ƒ

Where:

v = speed of the wave in m/s

λ = wavelength of the wave in m

ƒ = frequency of the wave in Hz

lambda

UNIVERSAL WAVE EQUATIONExample 2:

A sound wave produced at a frequency of 670 Hz travels a distance of 1220 m in 3.2 s.

a. What is the speed of the sound wave?

Solution:

v = d

t= 381 m/s

1220

3.2=

b. What is the wavelength of the wave?

λ =v

ƒ= 0.569 m

381.25

670=

UNIVERSAL WAVE EQUATION

Do Problems #36, 37, 43, 44 p. 318

Note: 1 nm = 10-9 m

1 Mm = 106 m

ELECTROMAGNETIC RADIATION

Light is a special form of waves that is created by changing electric and magnetic fields.

It does not require a “medium” as in other waves and travels at the speed of light (3.00 x 108 m/s)

Many different forms of electromagnetic radiation exists.

The only difference between the different forms is their frequency, wavelength and energy.

RADIO WAVES

Radiowaves are long wavelength, low frequency and low energy electromagnetic radiation.

They have all the properties of waves; they exhibit wave reflection, diffraction, and refraction.

They also show superposition properties and travel at the speed of light.

Do the Critical Thinking & Enrichment Worksheets.

WAVE INTERFERENCE

Do Water Wave Labs - Handouts

Discuss results of Water Wave Lab

Reflection Diffraction Refraction

Do “Water Wave Lab” (handout)

WAVE INTERFERENCE

Law of Superposition:

When two waves act on a single medium, the two waves will be “added” together to produce a single more complex wave.

Wave Superposition Demo

WAVE INTERFERENCE

Standing Waves

A special case of wave superposition.

It is caused by two waves of identical wavelength traveling in opposite directions along a single medium

Standing Wave Demo

Bridge Collapse – Standing Waves Gone Wild

WAVE INTERFERENCEResonance

Standing waves can occur at more than one frequency. These are called the natural or resonant frequencies of the cord.

Fundamental frequency or

First Harmonic

Second Harmonic

Third Harmonic

Forth Harmonic

L = ½ λ1

L = λ2

L = 3/2 λ3

L = 2 λ4

L = 5/2 λ5Fifth Harmonic

Anti-nodes

Nodes

WAVE INTERFERENCE

In general then:

L =n λn

2Where n = 1,2,3, …

(n labels the number of the harmonic)

Therefore:

λn =2 L

n

And since:

f =v

λn

fn =v

2 L

n

WAVE INTERFERENCE

fn =v

2 L

n

fn =v

2 Ln

For the fundamental frequency: f1

f1 =v

2 L(n = 1)

And each successive resonant frequency is an integer multiple of the fundamental frequency!

WAVE INTERFERENCE

f1 =v

2 L

Ex.A hollow 5.0 m long glass sound tube allow sound waves to travel through it at 320 m/s.a) Determine the fundamental frequency.

b) What is the resonant frequency of the fourth (n = 4) overtone?

=320

2 (5.0)= 32 Hz

f4 =4 x320

2 (5.0)= 128 Hz