Characteristics of WavesCharacteristics of Waves

PhysicsPhysicsFebruary 9, 2009February 9, 2009

Properties of WavesProperties of WavesLet’s Review:Let’s Review:

Two types of wavesTwo types of waves

1.1. Transverse Waves Transverse Waves

2.2. Longitudinal Waves Longitudinal Waves

Waves carry Waves carry energyenergy from one place to another. from one place to another.

Wave Speed = Wavelength x FrequencyWave Speed = Wavelength x Frequency

Periodic MotionPeriodic MotionSimple periodic motionSimple periodic motion is that motion in is that motion in which a body moves back and forth over a which a body moves back and forth over a fixed path, returning to each position and fixed path, returning to each position and velocity after a definite interval of time.velocity after a definite interval of time.

AmplitudeA

PeriodPeriod, T, is the time for one complete oscillation. (seconds,s)(seconds,s)

PeriodPeriod, T, is the time for one complete oscillation. (seconds,s)(seconds,s)

FrequencyFrequency, f, is the number of complete oscillations per second. Hertz (sHertz (s-1-1))

FrequencyFrequency, f, is the number of complete oscillations per second. Hertz (sHertz (s-1-1))

1f

T

Example:Example: The suspended mass makes 30 The suspended mass makes 30 complete oscillations in 15 s. What is the complete oscillations in 15 s. What is the

period and frequency of the motion?period and frequency of the motion?

x FF

15 s0.50 s

30 cylcesT

Period: T = 0.500 sPeriod: T = 0.500 s

1 1

0.500 sf

T Frequency: f = 2.00 HzFrequency: f = 2.00 Hz

A Transverse WaveA Transverse WaveIn a transverse wave, the vibration of the individual particles of the medium is perpendicular to the direction of wave propagation.

In a transverse wave, the vibration of the individual particles of the medium is perpendicular to the direction of wave propagation.

Motion of particles

Motion of wave

Longitudinal WavesLongitudinal Waves

In a In a longitudinal wavelongitudinal wave, the vibration of the , the vibration of the individual particles is parallel to the individual particles is parallel to the direction of wave propagation.direction of wave propagation.

In a In a longitudinal wavelongitudinal wave, the vibration of the , the vibration of the individual particles is parallel to the individual particles is parallel to the direction of wave propagation.direction of wave propagation.

Motion of particles

Motion of wave

v

Production of a Longitudinal WaveProduction of a Longitudinal Wave

• An oscillating pendulum produces An oscillating pendulum produces condensations condensations and and rarefactionsrarefactions that travel that travel down the spring.down the spring.

• The The wave length lwave length l is the distance is the distance between adjacent condensations or between adjacent condensations or rarefactions.rarefactions.

Water WavesWater Waves

An ocean wave is a combi-nation of transverse and longitudinal.

An ocean wave is a combi-nation of transverse and longitudinal.

The individual particles move in ellipses as the wave disturbance moves toward the shore.

The individual particles move in ellipses as the wave disturbance moves toward the shore.

Velocity and Wave Frequency.Velocity and Wave Frequency.The The period Tperiod T is the time to move a is the time to move a

distance of one wavelength. Therefore, distance of one wavelength. Therefore, the wave speed is:the wave speed is:

The The period Tperiod T is the time to move a is the time to move a distance of one wavelength. Therefore, distance of one wavelength. Therefore,

the wave speed is:the wave speed is:

1 but so v T v f

T f

The The frequency frequency ff is in s is in s-1-1 or or hertz hertz (Hz)(Hz)..

The The velocityvelocity of any wave is the of any wave is the product of the product of the frequencyfrequency and the and the

wavelengthwavelength::

v f

Velocity, Wavelength, Velocity, Wavelength, SpeedSpeed

Frequency Frequency f f = waves = waves per second (Hz)per second (Hz)

VelocityVelocity v v (m/s) (m/s)

sv

t

Wavelength Wavelength (m) (m)

v f

Wave Wave equationequation

Example 2:Example 2: An electromagnetic vibrator sends waves An electromagnetic vibrator sends waves down a string. The vibrator makes down a string. The vibrator makes 600600 complete cycles in complete cycles in

5 s5 s. For one complete vibration, the wave moves a . For one complete vibration, the wave moves a distance of distance of 20 cm20 cm. What are the frequency, wavelength, . What are the frequency, wavelength,

and velocity of the wave?and velocity of the wave?

600 cycles;

5 sf f = 120 Hzf = 120 Hz

The distance moved The distance moved during a time of one during a time of one

cycle is the wavelength; cycle is the wavelength; therefore:therefore:

= 0.020 m = 0.020 m

v = f

v = (120 Hz)(0.02 m)

v = 2.40 m/sv = 2.40 m/s

Sound WavesSound Waves

Source of Source of sound: a tuning sound: a tuning

fork.fork.

SoundSound is a is a longitudinal longitudinal mechanical wave mechanical wave that travels through that travels through an elastic medium.an elastic medium.

SoundSound is a is a longitudinal longitudinal mechanical wave mechanical wave that travels through that travels through an elastic medium.an elastic medium.

Imagine a room full of ping-pong balls…the molecules of air Imagine a room full of ping-pong balls…the molecules of air behave like tiny ping-pong balls. behave like tiny ping-pong balls.

All sound are produced by the vibration of objects. (piano or All sound are produced by the vibration of objects. (piano or guitar by vibrating strings, your voice by vibrating vocal cords)guitar by vibrating strings, your voice by vibrating vocal cords)

The vibrating object then sends a disturbance through a The vibrating object then sends a disturbance through a surrounding medium, usually air,surrounding medium, usually air,in the form of longitudinal waves.in the form of longitudinal waves.

Is there sound in the forest Is there sound in the forest when a tree falls?when a tree falls?

Based on our definition, Based on our definition, there there ISIS sound in the sound in the forest, whether a human forest, whether a human is there to hear it or not!is there to hear it or not!

Sound is a Sound is a physical physical disturbancedisturbance in an in an elastic medium.elastic medium.

Sound is a Sound is a physical physical disturbancedisturbance in an in an elastic medium.elastic medium.

The elastic medium (air) is required!

Sound Requires a MediumSound Requires a Medium

Evacuated Bell Jar

Batteries

Vacuum pump

The sound of a ringing bell diminishes as air The sound of a ringing bell diminishes as air leaves the jar. No sound exists without air leaves the jar. No sound exists without air molecules.molecules.

Graphing a Sound Wave.Graphing a Sound Wave.

Sound as a pressure wave

The sinusoidal variation of The sinusoidal variation of pressurepressure with with distancedistance is a useful way to represent a sound is a useful way to represent a sound

wave graphically. Note the wave graphically. Note the wavelengthswavelengths defined by the figure.defined by the figure.

Speed of SoundSpeed of Sound

0

m/s331 m/s 0.6

C cv t

Sound needs a medium to travel through. (solids, liquids, Sound needs a medium to travel through. (solids, liquids, and gases)and gases)

The speed of sound changes in different media and is The speed of sound changes in different media and is influenced by the surroundings.influenced by the surroundings.

Speed ≈ 330 m/s, but increases with humidity, and with Speed ≈ 330 m/s, but increases with humidity, and with temperature.temperature.

It is also faster in liquids, and much faster in solids.It is also faster in liquids, and much faster in solids.

Physics HomeworkPhysics Homework

ReadRead and and Take NotesTake Notes Chapter 25 and 26. Chapter 25 and 26.

DODO Problem Solving Practice Appendix F Problem Solving Practice Appendix F

(pp.683-684)(pp.683-684)

for both chapter 25 and 26for both chapter 25 and 26

Physics QuickyPhysics QuickyFebruary 10, 2009February 10, 2009

1.1. A person on a pier observes a set of ocean waves A person on a pier observes a set of ocean waves with a distance of 1.6 m b/w the crests. If a wave with a distance of 1.6 m b/w the crests. If a wave hits against the pier every 4 s, what is the frequency hits against the pier every 4 s, what is the frequency and speed of the wave?and speed of the wave?

2.2. Light waves travel in a vacuum at a speed of Light waves travel in a vacuum at a speed of 300,000 km/s. The frequency of visible light is about 300,000 km/s. The frequency of visible light is about 5 x 105 x 101414 Hz. What is the approx. wavelength of the Hz. What is the approx. wavelength of the light?light?

3.3. What is the wavelength of sound produced at a What is the wavelength of sound produced at a frequency of 300 Hz when the air temp is 20frequency of 300 Hz when the air temp is 20°C?°C?

Behavior of WavesBehavior of Waves

PhysicsPhysicsFebruary 10, 2009February 10, 2009

The Doppler The Doppler EffectEffect

An ambulance passing by, an airplane, or a fire truck siren…are An ambulance passing by, an airplane, or a fire truck siren…are all examples of the Doppler Effect.all examples of the Doppler Effect.

Relative motion creates a change in frequency, and therefore a Relative motion creates a change in frequency, and therefore a change in pitch.change in pitch.

You stand on the street while a someone drives by honking a You stand on the street while a someone drives by honking a horn. The pitch will be __________ as the car approaches you horn. The pitch will be __________ as the car approaches you and __________ as the car moves away.and __________ as the car moves away.

This phenomenon is common to all types of waves, including This phenomenon is common to all types of waves, including electromagnetic waves, such as visible light. electromagnetic waves, such as visible light.

Doppler EffectDoppler Effect

Doppler EffectDoppler Effect = =

Change of frequency due to the motion of source / Change of frequency due to the motion of source / receiverreceiver

Superposition of WavesSuperposition of WavesWhen two or more waves meet, they can When two or more waves meet, they can

either combine and have a greater either combine and have a greater magnitude (constructive interference) magnitude (constructive interference) or become smaller (destructive).or become smaller (destructive).

Interference affects the loudness of Interference affects the loudness of sounds (movie theatres, home sounds (movie theatres, home speaker system, etc.) speaker system, etc.)

Noise-cancelling earphones? Sound Noise-cancelling earphones? Sound compressions can be neutralized by compressions can be neutralized by mirror-image rarefactions in mirror-image rarefactions in earphones.earphones.

InterferenceInterference = =Pattern formed by overlapping of Pattern formed by overlapping of waveswaves

Behavior of WavesBehavior of WavesReflectionReflection = bouncing back of = bouncing back of

a wave that strikes the a wave that strikes the boundary b/w two mediaboundary b/w two media

Law of ReflectionLaw of Reflection

the angle of incidence = the the angle of incidence = the angle of reflectionangle of reflection

ΘΘ11 = = ΘΘ’’11

(note that it’s the angle with (note that it’s the angle with the normal)the normal)

Behavior of WavesBehavior of WavesRefractionRefraction = Change in = Change in

direction or bending of direction or bending of wave as it crosses the wave as it crosses the boundary b/w two media; boundary b/w two media;

wave travels at different wave travels at different speedsspeeds

Index of Refraction Index of Refraction

cc

n = n = --------

vv

Snell’s LawSnell’s Law

nn11 sin sinΘΘ11 = n = n22 sin sin ΘΘ22

If nIf n22 > n > n11, Snell’s Law tells us that , Snell’s Law tells us that ΘΘ22 < < ΘΘ11; that is the ; that is the

wave will bend (refract) toward the normal as it wave will bend (refract) toward the normal as it enters the medium. enters the medium.

Snell’s ExampleSnell’s Example

A beam of light in air is incident upon a piece of glass, A beam of light in air is incident upon a piece of glass, striking the surface at an angle of 30striking the surface at an angle of 30°. If the index °. If the index of refraction of the glass is 1.5, what are the angles of refraction of the glass is 1.5, what are the angles

of reflection and refraction?of reflection and refraction?

Behavior of WavesBehavior of WavesDiffractionDiffraction (Result of a wave around a barrier, such as (Result of a wave around a barrier, such as

an obstacle or the edges of an opening.)an obstacle or the edges of an opening.)

Standing WaveStanding Wave

(Incident [original] wave (Incident [original] wave

reflects back onto itself; reflects back onto itself;

nodes/antinodes)nodes/antinodes)

Behavior of WavesBehavior of Waves

DispersionDispersion (Separation of light into colors arranged (Separation of light into colors arranged according to frequency) Ex. Prismaccording to frequency) Ex. Prism

PolarizationPolarization (Aligning of vibrations in a transverse wave, (Aligning of vibrations in a transverse wave, usu by filtering out waves of other directions.)usu by filtering out waves of other directions.)

Physics HomeworkPhysics HomeworkFebruary 10, 2009February 10, 2009

Chapter 25 Review (p. 388)Chapter 25 Review (p. 388)# 6, 11, 12, 19, 24, 25, 31# 6, 11, 12, 19, 24, 25, 31

Chapter 26 Review (p. 401)Chapter 26 Review (p. 401)# 1, 6, 7, 21, 24, 33, 35# 1, 6, 7, 21, 24, 33, 35

Chapter 27 Review (p. 419)Chapter 27 Review (p. 419)# 4, 8, 19, 20, 24, 30# 4, 8, 19, 20, 24, 30

Electromagnetic Electromagnetic SpectrumSpectrum

PhysicsPhysicsFebruary 12, 2009February 12, 2009

Dispersion of LightDispersion of Light

When light strikes a prism, light of different wavelengths is bent When light strikes a prism, light of different wavelengths is bent at different angles as it moves into a refracting material.at different angles as it moves into a refracting material.

For instance, blue light (For instance, blue light (λλ≈470nm) bends more than red light ≈470nm) bends more than red light ((λλ≈650nm) ≈650nm)

Rainbows are created by dispersion of light in water droplets. Rainbows are created by dispersion of light in water droplets.

Electromagnetic SpectrumElectromagnetic Spectrum

Electromagnetic SpectrumElectromagnetic Spectrum transverse waves (does not require a medium) transverse waves (does not require a medium)

continuous range of waves extending from radio continuous range of waves extending from radio waves to gamma rays;waves to gamma rays;

differing in frequency and wavelength;differing in frequency and wavelength;

same speed, 3 x 10same speed, 3 x 1088 m/s in a vacuum m/s in a vacuum

The EM SpectrumThe EM SpectrumA wavelength of A wavelength of one nanometer 1 one nanometer 1 nm is:nm is:1 nm = 1 x 10-9 m1 nm = 1 x 10-9 m

Red 700 nm Red 700 nm Violet 400 Violet 400 nm nm

c = fc = 3 x 108 m/s

c = fc = 3 x 108 m/s

1024

1023

1022

1021

1020

1019

1018

1017

1016

1015

1014

1013

1012

1011

1010

109

108 107 106

105

104

Frequency wavelengthf (Hz) nm)

10-7 10-6

10-4

10-3

10-1

1 10 102

103

104

105

106

107

108

109

1010

1011

1012

1013

Gamma rays

X-rays

Infrared rays

Short Radio waves

Broadcast Radio

Long Radio waves

Ultraviolet

400 nm 400 nm 700 700 nmnm

Visible Visible SpectrumSpectrum

The Nature of LightThe Nature of Light

Physicists have studied light for centuries, Physicists have studied light for centuries, finding that it sometimes behaves as a finding that it sometimes behaves as a particle and sometimes as a wave. Actually, particle and sometimes as a wave. Actually, both are correct!both are correct!

Physicists have studied light for centuries, Physicists have studied light for centuries, finding that it sometimes behaves as a finding that it sometimes behaves as a particle and sometimes as a wave. Actually, particle and sometimes as a wave. Actually, both are correct!both are correct!

Reflection and Reflection and rectilinear rectilinear

propagation propagation (straight line path)(straight line path)

Dispersion of Dispersion of white light into white light into

colors.colors.

Lenses and OpticsLenses and Optics