Waves

Waves

A disturbance in a medium that transfers energy and momentum

To produce a Wave:

• A vibration (disturbance)

• A medium – a substance to travel through.

Examples of Waves

• Sound

• Light

• Water

There are two types of waves

Transverse – the individual wave particles move perpendicular to the velocity of the wave.

Examples:

Electromagnetic waves (light waves, radio waves, microwaves, x-rays)

Wave on a string

Longitudinal – the individual wave particles move parallel to the velocity of the wave.

Examples: Sound Waves

Parts of a wave:

Amplitude

Wavelength

Frequency – The number of wave cycles in 1 second.

Tf

1 Units 1/s = Hertz (Hz)

Wave Interference – The combination of two or more waves.

• Constructive interference – Two waves combine to make a bigger wave.

• Destructive interference – Two waves combine to make a smaller wave.

vTf

T1

fv1

wav

elen

gth

(m)

Period (s)

velocity

wavelength = (velocity)(Period)

fv

wav

elen

gth

(m)

frequency (hz)

The Wave Equation

fv v = velocity of the wave (m/s)

λ = wavelength (m)

f = frequency (1/s = Hz)

Example1: A sound wave has a frequency of 256 Hz. What is the wavelength? The speed of sound is 340m/s.

m

s

sm

f

v

fv

33.11

256

340

Example 2: A radio wave has a frequency of 96.9MHz. What is the wavelength? The speed of light is 3.0 x 108 m/s.

m

s

sm

f

v

fv

1.31

109.96

103

6

8

Standing Waves on a String

The velocity of a wave on the string depends on the mass per length of the string and the tension in the string.

LmF

v Tv = velocity of the wave (m/s)

FT= Tension in the string (N)

m = mass of the string (kg)

L = length of the string (m)

The fundamental frequency 1st Harmonic.

L2

v

f

fv

L

vf

21

L

The fundamental frequency 2nd Harmonic.

L

v

f

fv

L

vf 2

L

The fundamental frequency 3rd Harmonic.

L3

2

v

f

fv

L

vf

L

vf

2

332

3

3

L

The fundamental frequency 4th Harmonic.

2

L

v

f

fv

L

vf

Lv

f

22

4

4

L

The fundamental frequency 5th Harmonic.

L5

2

v

f

fv

L

vf

Lv

f

2

552

5

5

L

Summary

L

v

L

vf

L

v

l

vf

L

v

L

vf

L

v

L

vf

L

vf

2

5

25

2

24

2

3

23

22

2

5

4

3

2

1

fn=nf1

fn= nth harmonic

n = 1, 2 ,3, …..

f1 =1st harmonic (fundamental frequency)

Conditions for interference

L2

L1

P

δ = path difference = L2 – L1

Constructive Interference

δ = 0, λ, 2λ, 3λ …….

δ = nλ n = 0, 1, 2, 3, …

Destructive Interference

δ = λ/2, 3λ/2, 5λ/2 …….

δ = (n+ ½)λ

n = 0, 1, 2, 3, ….…

Sound Waves

• The speed of sound in air at room temperature is 340m/s.

• The speed of sound increases with increasing temperature.

• The speed of sound in water is 1500m/s.

• The speed of sound in aluminum is 5100m/s.

Physics Human

Perception

frequency

Intensity/Amplitude loudness

Pitch

Pressure fluctuations in air due to a vibrating tuning fork.

Applet

Frequency range of the human ear.

Ultra Sound

Human Ear

Sound intensity and the decibel scale

Beats

• Beats occur when two sound waves have slightly different frequencies interfere with one another.

• The number of beats per second is called the beat frequency.

• The beat frequency is determined by subtracting the two frequencies.

Standing Sound Waves in a Tube

• The wave travels at the speed of sound (340m/s)

• Open ends must have an antinode• Closed ends must have a node.• A pressure wave is set up in the tube.• A tube open at both ends acts just like the

string.• A tube closed at one end only has odd

harmonics.

Open Tube

3

23

LL21 L2

L

vf

L

vf

L

vf

2

3

2

3

2

1

Just like the string

Closed Tube

5

45

LL41

3

43

L

L

vf

L

vf

L

vf

4

54

34

5

3

1

Odd Harmonics

Resonance occurs when the driving frequency matches the natural frequency, resulting in large amplitude vibrations. Here are some examples of resonance

• Pushing someone on a swing.

• The Tacoma Narrows bridge.

• Breaking a wine glass with a sound wave

• Earthquakes totally destroying some buildings and not damaging others.

The Doppler Effect is a change in frequency (pitch) due to the relative motion of the sound source and observer.

• As the sound and listener approach each other the frequency is higher.

• As the sound and listener move away from each other the frequency is lower.

• The Doppler effect also occurs with light producing the red and green shift of distant stars.

• Doppler radar is used to track weather systems