Waves – Topic 4 Chapters 13, 14, 25, 26. Traveling Waves Wave Motion: Disturbance which travels in a medium transferring energy and momentum. –No Transfer.

Waves – Topic 4Waves – Topic 4

Chapters 13, 14, 25, 26Chapters 13, 14, 25, 26

Traveling WavesTraveling Waves

Wave MotionWave Motion: Disturbance which : Disturbance which travels in a medium transferring travels in a medium transferring energy and momentum.energy and momentum.– No Transfer of Mass!!!No Transfer of Mass!!!

Two ClassificationsTwo Classifications– Mechanical Waves (require a medium)Mechanical Waves (require a medium)

Ex: sound, water, Earth QuakesEx: sound, water, Earth Quakes

– Electromagnetic Waves (travel in vacuum)Electromagnetic Waves (travel in vacuum)Ex: light, microwaves – see chartEx: light, microwaves – see chart

Speed depends on MediumSpeed depends on Medium

Sound depends on Temp & Pressure Sound depends on Temp & Pressure

Strings/Springs depends on tension Strings/Springs depends on tension and linear mass densityand linear mass density

Electromagnetic waves all travel the Electromagnetic waves all travel the same speed in a vacuum. same speed in a vacuum. 3.0 x 103.0 x 1088

m/s. m/s.

Speed depends on MediumSpeed depends on Medium

Velocity of sound at STP is 330 m/s.Velocity of sound at STP is 330 m/s. (Standard Pressure and Temp.) (Standard Pressure and Temp.)STP - 1 atmosphere and 0˚Celsius. STP - 1 atmosphere and 0˚Celsius.

+/- 0.6 m/s for every 1˚C +/-+/- 0.6 m/s for every 1˚C +/-

At room temp. (22 degrees)At room temp. (22 degrees)v ≈ 343 m/sv ≈ 343 m/s

Table 14-1Table 14-1Speed of Sound in Various MaterialsSpeed of Sound in Various Materials

AluminumAluminum 64206420

GraniteGranite 60006000

SteelSteel 59605960

Pyrex glassPyrex glass 56405640

CopperCopper 50105010

PlasticPlastic 26802680

Fresh water (20 Fresh water (20 ººC)C) 14821482

Fresh water (0 Fresh water (0 ººC)C) 14021402

Hydrogen (0 Hydrogen (0 ººC)C) 12841284

Helium (0 Helium (0 ººC)C) 965965

Air (20 Air (20 ººC)C) 343343

Air (0 Air (0 ººC)C) 331331

MaterialMaterial Speed (m/s)Speed (m/s)

Reflection of PulsesReflection of Pulses

The pulse becomes inverted upon The pulse becomes inverted upon reflecting off the fixed end. reflecting off the fixed end.

Reflection at boundaryReflection at boundary The transmitted pulse is not inverted and The transmitted pulse is not inverted and

maintains the same phase. The reflected maintains the same phase. The reflected pulse is is also not inverted. pulse is is also not inverted.

Sound Sound isis

Longitudinal WaveLongitudinal WaveDisplacement of the particle is parallel to the Displacement of the particle is parallel to the propagation or direction of wave travel. propagation or direction of wave travel.

Light Light isis

Transverse Wave Transverse WaveDisplacement of the particle is at right angles to Displacement of the particle is at right angles to the propagation or direction of wave travel. the propagation or direction of wave travel.

Conceptual Checkpoint 14-2Conceptual Checkpoint 14-2How far away is the lightning?How far away is the lightning?

Echo ProblemEcho Problem

You shout at a canyon wall and here You shout at a canyon wall and here your echo 2.4 seconds after you your echo 2.4 seconds after you shout. How far away is the canyon shout. How far away is the canyon wall? Assume v = 343 m/swall? Assume v = 343 m/s

d = vtd = vt

d= 343m/s (1.2 sec) half the timed= 343m/s (1.2 sec) half the time d= 412 m to the wall.d= 412 m to the wall.

Wishing Well – Making a Splash!Wishing Well – Making a Splash!

How long after dropping the stone How long after dropping the stone will the boy hear the splash?will the boy hear the splash?

Making a Splash - SolutionMaking a Splash - Solution First calculate the time for the stone First calculate the time for the stone

to reach the water. d=vto reach the water. d=viit + ½gtt + ½gt22

t= 1.22 sect= 1.22 sec

Then calculate the time for the sound Then calculate the time for the sound wave to travel back up. d=vtwave to travel back up. d=vt

t= 0.02 sect= 0.02 sec

Add the two times. t= 1.24 secAdd the two times. t= 1.24 sec

PeriodicPeriodic WavesWaves - Terminology - Terminology FrequencyFrequency – – The number of vibrations or oscillations The number of vibrations or oscillations

per unit time. per unit time. Unit Hertz (Hz) – derived.Unit Hertz (Hz) – derived.

PeriodPeriod – – Time required for one complete cycle or to Time required for one complete cycle or to move the linear distance of one wavelength. move the linear distance of one wavelength. Unit second (s) – Fundamental.Unit second (s) – Fundamental.

AmplitudAmplitude – e – The maximum displacement of a particle The maximum displacement of a particle of the medium from the rest position. of the medium from the rest position. Unit meter (m)– Fundamental.Unit meter (m)– Fundamental.

WavelengthWavelength – – The distance traveled by one wave in The distance traveled by one wave in one period. The distance between two consecutive points in one period. The distance between two consecutive points in phase. phase. Unit Meter (m) – Fundamental.Unit Meter (m) – Fundamental.

Traveling Wave CharacteristicsTraveling Wave Characteristics

Frequency is the reciprocal of Period Frequency is the reciprocal of Period f = 1/T or T = 1/ff = 1/T or T = 1/f

Determine the frequency of a wave with a Determine the frequency of a wave with a period of 0.01667 sec.period of 0.01667 sec.

f =1/T , f = 1/ (0.01667 sec) = 60 Hzf =1/T , f = 1/ (0.01667 sec) = 60 Hz

What happens to the period of a wave as What happens to the period of a wave as its frequency increases?its frequency increases?

Wave Speed – wave equationWave Speed – wave equation Wave equation can be derived from the Wave equation can be derived from the

kinematics equation kinematics equation v = d/tv = d/t

If d=If d=λλ(wavelength) and t=T(period), then (wavelength) and t=T(period), then v= v= λλ/T/T

Since f = 1/T, thenSince f = 1/T, then

v = f v = f λλ

Wave SpeedWave Speed

A sound wave in a steel rail has a A sound wave in a steel rail has a frequency of 620 Hz and a frequency of 620 Hz and a wavelength of 10.5 m. what is the wavelength of 10.5 m. what is the speed of sound in steel?speed of sound in steel?

v=f v=f λλ v= 620hz (10.5 m)v= 620hz (10.5 m) v= 6510 m/sv= 6510 m/s

Periodic Wave PhenomenaPeriodic Wave Phenomena

Huygens Principle: - Wavelets!Huygens Principle: - Wavelets!– This principle uses the wave concepts to This principle uses the wave concepts to

explain periodic wave phenomena.explain periodic wave phenomena.ReflectionReflectionRefractionRefractionDiffractionDiffraction

Wave-frontsWave-fronts Sun Ripple Sun Ripple

ReflectionReflection Law of ReflectionLaw of Reflection

– The angle of The angle of incidence equals incidence equals the angle of the angle of reflection. reflection. ΘΘii = = θθrr

The incident and The incident and reflected rays lie in reflected rays lie in the same plane the same plane with the normal.with the normal.

RefractionRefraction Sudden change in direction of a wave as Sudden change in direction of a wave as

it changes speed.it changes speed.– It must enter obliquely to change direction! It must enter obliquely to change direction!

RefractionRefraction In both cases the speed of the wave has In both cases the speed of the wave has

decreased. This is indicated by the decreased. This is indicated by the decrease in wavelength! decrease in wavelength!

Refraction of SoundRefraction of Sound

When a wave slows down it bends closer to the When a wave slows down it bends closer to the normal. normal.

When a wave speed up it bends away from the When a wave speed up it bends away from the normal.normal.

DiffractionDiffraction

The bending or The bending or spreading out spreading out around the edges around the edges of a barrier or of a barrier or obstruction.obstruction.

Does the speed Does the speed change?change?

No! You can see No! You can see the wavelength is the wavelength is constant.constant.

DiffractionDiffraction

The extent of the The extent of the diffraction depends diffraction depends on the ratio of the on the ratio of the wavelength to the wavelength to the opening of the opening of the hole.hole.

Diffraction ~ λ/DDiffraction ~ λ/D Tsunami WavesTsunami Waves

InterferenceInterference

Constructive Interference Destructive InterferenceConstructive Interference Destructive Interference

Waves DO NOT bounce! Energy passes through.Waves DO NOT bounce! Energy passes through.

SuperpositionSuperposition

The Algebraic sum of the amplitudes The Algebraic sum of the amplitudes of two or more waves which form of two or more waves which form interference.interference.

Waves which arrive in phase form Waves which arrive in phase form constructive interference.constructive interference.

Waves which meet out of phase form Waves which meet out of phase form destructive interference.destructive interference.

Standing or Standing or Stationary WavesStationary Waves

Conditions need:Conditions need:– Same AmplitudeSame Amplitude– Same frequencySame frequency– Opposite DirectionsOpposite Directions

Caused by both Constructive and Caused by both Constructive and Destructive interference.Destructive interference.– Nodes – DestructiveNodes – Destructive– Antinodes - ConstructiveAntinodes - Constructive

HarmonicsHarmonics

Vibrating strings or pipes form Vibrating strings or pipes form Stationary wave patterns each Stationary wave patterns each pattern refers to a different pattern refers to a different Harmonic.Harmonic.

BeatsBeats

When two frequencies are very close When two frequencies are very close they interfere creating a beat sound.they interfere creating a beat sound.

Beat frequency = F1 –F2 Beat frequency = F1 –F2

Figure 14-22Figure 14-22Interference with Two SourcesInterference with Two Sources

InterferenceInterference

Path Diff = n λ, Constructive Int.Path Diff = n λ, Constructive Int.

Doppler EffectDoppler Effect

EEEEEEEEEE OOOOOOOOOOOOOO

Movement toward or decreasing distance produced a Movement toward or decreasing distance produced a higher frequency.higher frequency.

Figure 14-15Figure 14-15The Doppler Effect: A Moving ObserverThe Doppler Effect: A Moving Observer

Doppler Effect Doppler Effect What happens when the moving source reaches or exceeds the speed of the wave?

The Doppler Effect and Sonic Booms

Plane-Mach1

ResonanceResonance

Is it Live or is it Memorex –viewed Is it Live or is it Memorex –viewed under a strobe lightunder a strobe light

An Incredibly Irritating Resonance DeAn Incredibly Irritating Resonance Demonstrationmonstration

Resonating Wave – Match the λResonating Wave – Match the λ

Tacoma Narrows BridgeTacoma Narrows Bridge

On November 7, 1940, at approximately On November 7, 1940, at approximately 11:00 AM, the first Tacoma Narrows 11:00 AM, the first Tacoma Narrows suspension bridge collapsed due to wind-suspension bridge collapsed due to wind-induced vibrations.induced vibrations.

Situated on the Tacoma Narrows in Puget Situated on the Tacoma Narrows in Puget Sound, near the city of Tacoma, Sound, near the city of Tacoma, Washington, the bridge had only been Washington, the bridge had only been open for traffic a few months. open for traffic a few months.