WavesWavesA propagation of A propagation of energy through a energy through a medium without a medium without a

transfer of the transfer of the medium.medium.

Two Types of WavesTwo Types of Waves1) Transverse Wave – a wave where the disturbance of the 1) Transverse Wave – a wave where the disturbance of the

medium is perpendicular to the direction of energy medium is perpendicular to the direction of energy motion.motion.

Transverse Wave DiagramTransverse Wave Diagram Transverse Diagram 1Transverse Diagram 1 Transverse Water WaveTransverse Water Wave Transverse Wave Animation Transverse Wave Animation Transverse Wave AnimationTransverse Wave Animation 1 1

2)2) Longitudinal Wave (Compression Wave) – a wave where Longitudinal Wave (Compression Wave) – a wave where the disturbance of the medium is parallel to the direction the disturbance of the medium is parallel to the direction of energy motion.of energy motion.

Sound is a longitudinal wave.Sound is a longitudinal wave.Longitudinal Wave 1Longitudinal Wave 1Longitudinal Wave 2Longitudinal Wave 2Longitudinal Wave 3Longitudinal Wave 3Longitudinal Wave AnimationLongitudinal Wave Animation

Compression – a region of high density in a longitudinal waveCompression – a region of high density in a longitudinal waveRarefaction – a region of low density in a longitudinal waveRarefaction – a region of low density in a longitudinal waveThe amplitude is represented by the amount of compression (density).The amplitude is represented by the amount of compression (density).

• Surface Wave – A combination of transverse and longitudinal Surface Wave – A combination of transverse and longitudinal waves.waves.Surface Wave Surface Wave

wavelength (λ)

crest

trough

amplitude

EquilibriumPosition

Components of a Transverse Wave

• Crest: the location of maximum displacement on a wave.• Trough: the location of the lowest displacement on a wave.• Equilibrium position: the undisturbed position of the medium• Amplitude: the displacement from the equilibrium position to crest or trough. The amplitude represents the energy in a wave.• Wavelength (λ): the distance between the same two locations on adjacent waves.

Wave PulseWave Pulse• A single disturbance in the mediumA single disturbance in the medium

Wave Pulse AnimationWave Pulse Animation

Wave PulseWave Pulse

Periodic WavePeriodic Wave• A repetitious wave.

Transverse Wave

Two categories of wavesTwo categories of waves

Matter Wave (Mechanical Wave) – a Matter Wave (Mechanical Wave) – a wave that needs a medium to travel wave that needs a medium to travel throughthroughExamples: EarthquakeExamples: Earthquake The Earthquake Shake The Earthquake Shake

A vibrating guitar stringA vibrating guitar string

The surface of waterThe surface of water WaterWater Surface Wave Surface Wave

Electromagnetic Wave – a wave that Electromagnetic Wave – a wave that does not need a medium to travel does not need a medium to travel throughthrough

Example: Radio waves, TV waves, light, x-raysExample: Radio waves, TV waves, light, x-rays Electromagnetic WavesElectromagnetic Waves

Speed of a WaveSpeed of a Wave

T =period: the amount of time for one wave to be created.

wavelength (λ)

v=d/t = λ /T v=λ / T

f = frequency: the number of waves created in one second. •Frequency is measured in Hertz (Hz) which has the fundamental unit of s-1 (1/s)

T=1/f v=fλ•Example: What is the speed of the wave above if its created in 4.0 s •and has a wavelength of 12.0 m?

v=λ/T = 12.0 m / 4.0s = 3.0 m/s

Speed of a wave (cont.)Speed of a wave (cont.)

d

v=d/t

λ

f= #waves / time v=fλThe above waves are created in 6.0 s and has a wavelength of 9.0 m. What is the speed of the waves?

f=3 waves/6.0s =.50 Hz v=fλ=(.50 Hz)(9.0m)=4.5 m/s

Wave PropertiesWave Properties

• Speed: Unchanged as it travels through a medium. The wave speed is dependent only on the properties of the medium.

• Frequency: IncreasedFrequency: Increased Wavelength: Wavelength: DecreasesDecreases

In one medium:

• Frequency: Decreased Wavelength: Increases

A larger frequency of cars:

A smaller frequency of cars:

A graphical explanation of why wavelength is dependent on speed:

The speed of the vehicle are constant.

Mathematical explanation Mathematical explanation of why wavelength varies of why wavelength varies

with speed:with speed:

v = f λ

v

v =

= ff

λ

λ

Large frequency, short wavelength

Small frequency, long wavelength

Speed remains constant in a medium.

Wave Properties between Wave Properties between MediaMedia

Incident wave

reflected wavetransmitted wave

Medium 1

Medium 2

Incident wave: The original wave that approaches the boundary between two media.Reflected wave: The portion of the wave redirected back into the first medium.Transmitted wave: The portion of the original wave that the transferred into the new

medium.

The more similar the properties between the two media the more of the wave that is transmitted.

Wave Reflection

Phase of the Reflected Phase of the Reflected WaveWavephase – the position of a wave.

inverted wave (180º phase shift) erect wave (0º phase shift)

incident wave

Reflected wave is inverted

incident wave

reflected wave

Reflected wave is erect

If the new medium is more dense than the previous medium, the reflected wavewill be inverted.

If the new medium is less dense than the previous medium, the reflected wavewill be erect.

reflected wave

incident wave

Wave Wave InterferenceInterferenceInterference- The interaction between two or more waves Interference- The interaction between two or more waves

simultaneously occupying the same location.simultaneously occupying the same location.Principle of superposition – the algebraic sum of two or more Principle of superposition – the algebraic sum of two or more waves.waves.

Constructive interference will occur in the following situation when the waves occupythe same position at the same time.

A B

A+BConstructive interference

The principle of superposition shows the resulting wave of both Interfering.

B A

The wave continue traveling in the same direction unaffected by the wave interference.

Destructive interference will occur in the following situation when the waves occupythe same position at the same time.

A

B

A+B Destructive interferenceThe principle of superposition shows the resulting wave of both Interfering.

B

A

The waves continue travelingin the same direction unaffectedby the wave interference.

Total Destructive interference will occur when two waves with equal magnitude, butopposite directions interfere as show below.

AB

After the interference the waves continue traveling In the same direction unaffected by the interference.

A+B

B

A

End

Amplitude: Decreases

Wavelength: Changes

Speed: Changes

Frequency: Constant

Wave Component Properties Traveling between Media

Wave Wave PhenomenaPhenomena

Standing WaveStanding WavessFluctuating stationary waves formed by the interference of traveling waves of the same frequency, speed and amplitude moving in opposite directions.

Standing Wave Diagram

Standing Wave Animation 1

Standing Wave Animation 2

Standing Wave Animation 3

Standing wave demonstration

Standing Wave Animation

Wave FrontsWave Fronts

wave front: a short hand notation of representing thecrest of a wave.

Law of ReflectionLaw of Reflection

Normal: a perpendicularto the surface of an object.

Barrier

θr

The angle of incidence is equal to the angle of reflection. (θi=θr)

θi

Incident wave

Reflected wave

θi=angle of incidence

θr=angle of reflection

RefractionRefraction The change in direction of a wave when traveling The change in direction of a wave when traveling

from one medium to another.from one medium to another.

wave direction in medium 1

wave direction

in medium 2

medium 1medium 2

DiffractionDiffractionDiffraction: the bending and spreading of a wave that passes through an opening or around an obstacle. •The smaller the opening compared the wavelength of the wave, the greater the •diffraction.

Diffraction

SoundSound

Audible frequency range: 20 Hz to 20 kHzAudible frequency range: 20 Hz to 20 kHz Infrasonic region: Frequencies less than 20 Infrasonic region: Frequencies less than 20

HzHz Ultrasonic region: Frequencies above 20 kHzUltrasonic region: Frequencies above 20 kHz The ultrasonic region limit is 1 GHz.The ultrasonic region limit is 1 GHz.

The vibration of air molecules in a medium perceivable by the human ear.

• Sound in air is a longitudinal wave.• Sound in a liquid or gas is primarily longitudinal, but contains a small fraction of a

traverse wave component.

Pitch – how the frequencies of sound is perceived.

Speed of SoundSpeed of Sound The speed of sound in air at 0ºC is 331 The speed of sound in air at 0ºC is 331

m/s.m/s. The speed of sound increases as The speed of sound increases as

temperature increases.temperature increases. v=(331m/s +.6Tc) for environmental v=(331m/s +.6Tc) for environmental

temperatures.temperatures. v=331m/s(1+Tc/273m/s)v=331m/s(1+Tc/273m/s)1/21/2 for higher for higher

temperatures. temperatures. Mach number: A multiple of the speed of sound

Example: Mach 2 at 0ºC is 662 m/s.

What is the speed of a jet traveling at Mach 3 at 0º?993 m/s

The Doppler EffectThe Doppler Effect

The perceived frequency change of sound The perceived frequency change of sound because of a wavelength change due to because of a wavelength change due to relative motion between a source and an relative motion between a source and an observer.observer.

s

oso vv

vvff

v = speed of sound at a given temperaturevo = speed of the observer of the soundvs = speed of the source of the sound

numerator: + source moving towards observer - source moving away from observer

denominator: - observer moving towards source + observer moving away from source

ResonanceResonance

A matched frequency between a A matched frequency between a source and an object which causes source and an object which causes increased oscillation vibrations of increased oscillation vibrations of the object.the object.

BeatsBeats

Fluctuations in intensity between Fluctuations in intensity between two sound frequencies due two sound frequencies due constructive and destructive constructive and destructive interference of the sound waves.interference of the sound waves.

ffbb=|f=|f11-f-f22||

ffbb:beat frequency:beat frequency