Physical Science

Physical SciencePhysical Science

WavesWaves

Slides subject to changeSlides subject to change

Energy TransferEnergy Transfer

A wave is a A wave is a disturbance disturbance that propagates that propagates through space through space and time.and time.

Waves transfer Waves transfer energyenergy..

Sinking rock does work pushing Sinking rock does work pushing surface water aside. Energy surface water aside. Energy transferred to water.transferred to water.

Water surface molecules push Water surface molecules push nearby molecules ...nearby molecules ...

Wave “propagates” through the Wave “propagates” through the water.water.

Longitudinal WaveLongitudinal Wave

Longitudinal waveLongitudinal wave: Particles move in same : Particles move in same direction as the wave.direction as the wave.

Examples: Sound waves, “Slinky” spring.Examples: Sound waves, “Slinky” spring.

Animation courtesy of Dr. Dan Russell, Kettering University Animation courtesy of Dr. Dan Russell, Kettering University

Transverse WaveTransverse Wave

Transverse waveTransverse wave: Particles move : Particles move perpendicular to wave direction.perpendicular to wave direction.

Examples: Examples: Electromagnetic waves (Electromagnetic waves (radio, radio, television, optical), waves on a string.television, optical), waves on a string.

Animation courtesy of Dr. Dan Russell, Kettering University Animation courtesy of Dr. Dan Russell, Kettering University

Wave PropertiesWave Properties

A A mediummedium propagates waves. propagates waves. AmplitudeAmplitude is the maximum displacement is the maximum displacement

from equilibrium.from equilibrium.

PeriodPeriod

PeriodPeriod ( (TT ), is the time between ), is the time between successive peaks.successive peaks.

Time tTime t

PeriodPeriod

time time →→

““Period” is the Period” is the timetime between successive between successive peaks (or wave peaks (or wave crests).crests).

FrequencyFrequency

FrequencyFrequency is the rate at which peaks are is the rate at which peaks are arriving. arriving.

Units are generally events per time, such Units are generally events per time, such as revolutions per minute. Cycles per as revolutions per minute. Cycles per second units are called Hertz (Hz).second units are called Hertz (Hz).

ExamplesExamples Surfer waves: 4 crests per minute.Surfer waves: 4 crests per minute. Electrical Outlet: 60 HzElectrical Outlet: 60 Hz

Music

Music “middle C” 262 Hz (cycles per Music “middle C” 262 Hz (cycles per second).second).

Relate Period and FrequencyRelate Period and Frequency

If middle C is 262 Hz, what is the time between crests?If middle C is 262 Hz, what is the time between crests? Given Given FormulaFormula f = 262 Hzf = 262 Hz ff = 1/ = 1/TT

thereforetherefore, 262 = 1/T, T, 262 = 1/T, T = 0.0038 seconds = 0.0038 seconds

ff = 1/ = 1/TT

WavelengthWavelength

Associated with a traveling wave.Associated with a traveling wave. WavelengthWavelength ( (λλ) ) is the distance between is the distance between

successive crests.successive crests. Traveling WaveTraveling Wave

Wavelength is the Wavelength is the distance between crests.distance between crests.

SoundSound

The speed of sound is 344 m/s under The speed of sound is 344 m/s under standard conditions in air (sea level, 20 °C).standard conditions in air (sea level, 20 °C).

That’s about 768 mph.That’s about 768 mph.

Wave speed = wavelength times frequencyWave speed = wavelength times frequency

vv = = λλ f f

WavelengthWavelength

If the frequency of a concert tone is 262 Hz, If the frequency of a concert tone is 262 Hz, what is the wavelength what is the wavelength λλ??

GivenGiven FormulaFormula v = 344 m/sv = 344 m/s v = v = λλ f f f = 262 Hzf = 262 Hz

v = v = λλ f f 344 = 344 = λλ(262)(262) λλ = 1.31 m = 1.31 m

Electromagnetic WavesElectromagnetic Waves

The wave, or "disturbance," is a The wave, or "disturbance," is a transversetransverse electric field, which is invisible. electric field, which is invisible. Causes charged particles to move.Causes charged particles to move.

Light, microwaves, x-rays, TV, and Light, microwaves, x-rays, TV, and radio transmissions are various radio transmissions are various kinds of electromagnetic waves. kinds of electromagnetic waves.

The electric field interacts with The electric field interacts with electrons and protons.electrons and protons.

Electromagnetic WavesElectromagnetic Waves

Speed of light Speed of light cc = 3.0x10 = 3.0x1088 m/s m/s

KFI AM radio broadcasts atKFI AM radio broadcasts at f f = 640 kHz. What = 640 kHz. What is the wavelength?is the wavelength?

GivenGiven FormulaFormula vv = 3.0x10 = 3.0x1088 m/s m/s v = v = λλ f f ff = 640 kHz = 640x10 = 640 kHz = 640x1033 Hz Hz

3x103x108 8 = = λλ (640x10 (640x1033)) λλ = 470 m = 470 m Radio wavelength is important in antenna design.Radio wavelength is important in antenna design.

RadarRadar

Icebergs on ship radarIcebergs on ship radar Aircraft search radarAircraft search radar

WikipediaWikipedia

Sound Wave CharacteristicsSound Wave Characteristics

Sound is propagation of compression waves Sound is propagation of compression waves through matter (through matter (solidsolid, , liquidliquid, or , or gas)gas)..

Three regions.Three regions. Ultrasonic > 20,000 Hz (medicine, some Ultrasonic > 20,000 Hz (medicine, some

animals – dogs, bats – can hear)animals – dogs, bats – can hear) Audible 20 Hz – 20,000 Hz, (human hearing) Audible 20 Hz – 20,000 Hz, (human hearing)

Age TestAge Test Infrasonic < 20 Hz (earthquakes, some Infrasonic < 20 Hz (earthquakes, some

animals – cattle, elephants - can hearanimals – cattle, elephants - can hear or feel or feel?)?)

IntensityIntensity

Measure intensity = rate of energy transfer Measure intensity = rate of energy transfer through a given area (power/area = W/mthrough a given area (power/area = W/m22).).

Sound IntensitySound Intensity Minimum intensity human can hear is Minimum intensity human can hear is

about 10about 10-12-12 W/m W/m22, the , the threshold of threshold of hearinghearing ... ... a mosquito at 10 feet!a mosquito at 10 feet!

Intensity decreases the farther you are Intensity decreases the farther you are from the source. Goes as 1/rfrom the source. Goes as 1/r22..

Sound LoudnessSound Loudness

Loudness, in bels (after Alexander Grahm Loudness, in bels (after Alexander Grahm Bell), of a sound of intensity I is defined to be Bell), of a sound of intensity I is defined to be

II00 is the minimum intensity detectable by the is the minimum intensity detectable by the

human ear.human ear.

0

logI

IL


Logarithms are powers of 10.Logarithms are powers of 10. If a sound is 100 times more intense than If a sound is 100 times more intense than

another, its loudness is 2 bels more (factor another, its loudness is 2 bels more (factor of 100 or 10of 100 or 1022))

If one sound is 6 bel, and another is 9 bel, If one sound is 6 bel, and another is 9 bel, it is 1000 times more intense (10it is 1000 times more intense (1033).).


The bel is a large unit, so a sub-unit, the The bel is a large unit, so a sub-unit, the decibeldecibel, is generally used. , is generally used.

If one sound is 100 times louder than If one sound is 100 times louder than another, it is 2 bels or 20 dB louder.another, it is 2 bels or 20 dB louder.

0

log10I

ILdecibels

Intensity LevelsIntensity Levels

Think Think POWERS OF TENPOWERS OF TEN Threshold of hearing 0 dB, Threshold of hearing 0 dB, a mosquito 10 a mosquito 10

feet away.feet away. Humming of a refrigerator 40 db (10Humming of a refrigerator 40 db (1044 · · II00))

Conversation 60 dB (10Conversation 60 dB (1066 · · II00).).

Leaf blower user 90 dB (10Leaf blower user 90 dB (1099 · · II00). ).

Rock band 110 dB (10Rock band 110 dB (101111 · · II00).).

Typical ProblemTypical Problem

A subway train has loudness 90 dB.A subway train has loudness 90 dB. Rock band loudness of 110 dB.Rock band loudness of 110 dB. How many times greater is the sound intensity How many times greater is the sound intensity

of the band than that of the train?of the band than that of the train?

The rock band is 20 dB louderThe rock band is 20 dB louder Divide dB by 10Divide dB by 10 20/10 = 220/10 = 2 Intensity is 10Intensity is 1022 or 100 times greater. or 100 times greater.

Harmful Impact of SoundHarmful Impact of Sound

Sounds of less than 75 decibels, even after long Sounds of less than 75 decibels, even after long exposure, are unlikely to cause hearing loss.exposure, are unlikely to cause hearing loss.

Exposure to harmful sounds causes damage to the Exposure to harmful sounds causes damage to the sensitive hair cells of the cochlea – the inner ear.sensitive hair cells of the cochlea – the inner ear.

Hearing injured by noise Hearing injured by noise From an intense brief impulse, such as an From an intense brief impulse, such as an

explosion.explosion. From From continuouscontinuous exposure to noise, such as in a exposure to noise, such as in a

woodworking shop.woodworking shop.

More on Hearing LossMore on Hearing Loss

The The decibel leveldecibel level and and time of exposuretime of exposure are the most important considerations.are the most important considerations.

Some sounds – artillery, explosions – Some sounds – artillery, explosions – are so loud (+140 db), ANY brief are so loud (+140 db), ANY brief exposure to them at close range can exposure to them at close range can cause permanent damage and cause permanent damage and hearing loss.hearing loss.

More on Hearing LossMore on Hearing Loss

Sounds at 100 decibels (such as loud Sounds at 100 decibels (such as loud music through stereo headphones) will music through stereo headphones) will take a while longer (1-2 hours of take a while longer (1-2 hours of exposure) to cause permanent damage.exposure) to cause permanent damage.

Ipods are tested by Apple up to 103 db.Ipods are tested by Apple up to 103 db.

Standing Waves

Mode of vibration in a string or column of air with unique pattern.

Traveling wave that reflects off an end in such a way that the medium appears to vibrate in segments or regions.

Standing wave animation.

Fundamental Frequency

The frequency when this pattern appears is the fundamental frequency, or “first harmonic.”

This is the primary frequency you hear when you pluck a guitar string.

λλ/2/2

Second Harmonic

Double the frequency and the “second harmonic” appears.

λλ/4/4 λλ/4/4

Higher Harmonics

Many oscillators, including the human voice or a bowed violin string are composed of harmonics.

The quality, or timbre of that sound is a result of the relative strengths of the individual harmonic frequencies.

ResonanceResonance

All oscillators have a natural frequency.All oscillators have a natural frequency. Add energy in synch with that natural Add energy in synch with that natural

frequency results in frequency results in resonanceresonance.. Example: A swing.Example: A swing.

ResonanceResonance Tacoma Narrows Bridge, WA (1940)Tacoma Narrows Bridge, WA (1940)

Doppler Frequency ShiftDoppler Frequency Shift

Source moves towards you, waves are Source moves towards you, waves are bunched up, you hear higher pitch.bunched up, you hear higher pitch.

Source moves away from you, waves are Source moves away from you, waves are stretched out, you hear lower pitch.stretched out, you hear lower pitch.

Fire engineFire engine

TrainTrainHigher pitch hereHigher pitch here

Lower pitch hereLower pitch here

Beat FrequenciesBeat Frequencies

If two sound waves arrive at our ears If two sound waves arrive at our ears simultaneously.simultaneously. Our ears hear the average frequency of the two Our ears hear the average frequency of the two

waves.waves. Also hear the intensity increase and decrease – Also hear the intensity increase and decrease –

wavering beats.wavering beats.

ffbeatbeat = = ff11 – – ff22

Musicians use beat phenomena to tune their Musicians use beat phenomena to tune their instruments. instruments. Standard for musical pitch A = 440 Hz.Standard for musical pitch A = 440 Hz.

Speed of SoundSpeed of Sound

vvsoundsound = 344 m/s or 1,126 ft/s (770 mi/h) at = 344 m/s or 1,126 ft/s (770 mi/h) at

sea level and 20 sea level and 20 °C°C.. Time for sound to go 1.0 mile = 4.7 s.Time for sound to go 1.0 mile = 4.7 s.

How far is a thunderstorm? Count out How far is a thunderstorm? Count out seconds between lightning and thunder.seconds between lightning and thunder.

One mile approximately every 5 seconds.One mile approximately every 5 seconds. vvsoundsound varies with temperature: if air warmer, varies with temperature: if air warmer,

sound goes faster.sound goes faster.

Boat moving in water faster than waves Boat moving in water faster than waves can propagate.can propagate.

Forms a V−shaped wake, sometimes even Forms a V−shaped wake, sometimes even from the stern of the boat.from the stern of the boat.

Move Faster Than the WaveMove Faster Than the Wave

Pressure wave Pressure wave build-up.build-up.

Sound BarrierSound Barrier

WikipediaWikipedia

Pressure wave Pressure wave build-upbuild-up

High−performance aircraft speeds measured in High−performance aircraft speeds measured in Mach numbers.Mach numbers.

Mach 1.0 = speed of sound.Mach 1.0 = speed of sound.

Bell X-1Bell X-1

Chuck Yeager breaks sound barrier, Oct 14, 1947. Chuck Yeager breaks sound barrier, Oct 14, 1947. Mojave Desert. Mach 1.06.Mojave Desert. Mach 1.06.

SupersonicSupersonic Concorde supersonic transport (SST).Concorde supersonic transport (SST). Mach 2.04 (1,350 mph) cruising speed.Mach 2.04 (1,350 mph) cruising speed. You can't hear the sonic "boom" if you are You can't hear the sonic "boom" if you are

inside. Why?inside. Why? First flown 1969.First flown 1969. Crash in Paris July 25, 2000.Crash in Paris July 25, 2000. Last flight October 2003.Last flight October 2003.

Design characteristics inside.Design characteristics inside.

What it felt like inside.What it felt like inside.

Concord take off

Sonic BoomSonic Boom

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