1 f = Τ. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by

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2 result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by 1 f = Τ amplitude (how far do the bits move from their equilibrium positions? Amplitude of MEDIUM) periodor frequency (how long does it take for each bit to go through one cycle?) wavelength (over what distance does the cycle repeat in a freeze frame?) v= λ f wave speed (how fast is the energy transferred?)

3 Types of Waves Sound String

4 Sound is a Longitudinal Wave Pulse Tuning Fork Guitar String

5 is a Pressure Wave

6 Spherical Waves

7 Wavelength and Frequency are Inversely related: The shorter the wavelength, the higher the frequency. The longer the wavelength, the lower the frequency. f = v λ 3Hz 5Hz

8 Wave speed: Depends on Properties of the Medium: Temperature, Density, Elasticity, Tension, Relative Motion v = λ f

9 The speed of sound waves in a medium depends on the compressibility, density and temperature of the medium The compressibility can sometimes be expressed in terms of the elastic modulus of the material The speed of all mechanical waves follows a general form: Liquid or Gas: Solid Rod: v v = = B ρ Y ρ v = v = T ρ v = λ f elastic property inertial property (1D string) Dependence on Temperature: T v = + o C (331 m/s) C

343 m/s in Air @ 20 C 5960 m/s in Steel @ 20 C 1522

10 343 m/s in 20 C 5960 m/s in 20 C 1522 m/s in Ocean 20 C Speed of Sound in a Vacuum?

11 v = sound 343 m/s Problem: You see lightening flash and 10 seconds later you hear the thunder clap. How far away was the lighting from your position? d = vt (343 m/ s)10 = s = 3.43km ~2 miles (Rule of thumb: divide time by 5 to get miles)

12 Speed of wave depends on properties of the MEDIUM v = λ f Speed of particle in the Medium depends on SOURCE: SHM vt () = Aω sinωt

13 Waves on Strings v = λ f v = μ = F (1D string) μ m/ L (linear mass density)

14 Problem: v = λ f The displacement of a vibrating string vs position along the string is shown. The wave speed is 10cm/s. If the linear density of the string is.01kg/m, what is the tension of the string?

15 Problem: v = F m/ L The displacement of a vibrating string vs position along the string is shown. The wave speed is 10cm/s. If the linear density of the string is.01kg/m, what is the tension of the string? F = v 2 ( m/ L) 2 5 F = (.1 m) (.01 kg/ m) = 10 N

16 Problem: v = F m/ L The displacement of a vibrating string vs position along the string is shown. The wave speed is 10cm/s. If the the tension doubles, how does the wave speed change? v 2 = F2 m/ L 2F = = m/ L 2v Wave speed increases by a factor of 2

17 Wave PULSE: traveling disturbance transfers energy and momentum no bulk motion of the medium comes in two flavors LONGitudinal TRANSverse

18 Reflected PULSE: If the end is bound, the pulse undergoes an inversion upon reflection: a 180 degree phase shift If it is unbound, it is not shifted upon reflection. Free End Bound End

19 Reflection of a Wave Pulse

20 Pulsed Interference

21 Superposition Waves interfere temporarily.

22 Reflection of a Traveling Wave

23 Superposition Waves ADD in space. Simply add them point by point.

24 Superposition of Sinusoidal Waves Case 1: Identical, same direction, with phase difference (Interference) Case 2: Identical, opposite direction (standing waves) Case 3: Slightly different frequencies (Beats)

25 Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase

26 Interference of Sound Waves Sound waves interfere Constructive interference occurs when the path difference between two waves motion is zero or some integer multiple of wavelengths path difference = nλ Destructive interference occurs when the path difference between two waves motion is an odd half wavelength path difference = (n + ½)λ

27 Interference

28 Chapter 14 Problem 26

29 Interference: Beats beats frequency = difference in frequencies

30 Interference: Beats Amplitude ~ Power ~ Loudness

31 Interference: Beats f = f f f B ave = 2 1 f + f 2 1 2

32 Beats Two tuning forks have frequencies of 440Hz and 438 Hz. What average frequency will you hear and what is the beat frequency?

33 Beats Two tuning forks have frequencies of 440Hz and 438 Hz. What average frequency will you hear and what is the beat frequency? f = f f f = B 2 1 ave f + 2 f 2 1 f ave f2 + f1 440Hz + 438Hz = = = Hz fb = f2 f1 = 440Hz - 438Hz = 2Hz

34 Standing Waves: Boundary Conditions

35 Node & Antinodes A node occurs at a point of zero amplitude nλ x = n = 0,1, K 2 An antinode occurs at a point of maximum displacement, 2A nλ x = n = 1, 3, K 4

36 Transverse Standing Wave Produced by the superposition of two identical waves moving in opposite directions.

37 Standing Waves Standing waves form in certain MODES based on the length of the string or tube or the shape of drum or wire. Not all frequencies are permitted!

38 Standing Waves on a String Harmonics

39 Standing Waves on a String λ = 2L 1 λ = L 2 λ = 3 2L 3

40 Standing Waves on a String λ = n 2L n f n = v/ λ n v f = n n 2 L

41 Standing Wave on a String Problem A string with a mass of 8.00 g and a length of 5.00 m has one end attached to a wall; the other end is draped over a pulley and attached to a hanging object with a mass of 4.00 kg. If the string is plucked, what is the fundamental frequency of vibration?

42 You Try Standing Waves A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is g/cm, and its tension is 600 N, what is the fundamental frequency? a. 316 Hz b. 632 Hz c. 158 Hz d. 215 Hz e. 79 Hz

43 The possible frequency and energy states of a wave on a string are quantized. f 1 Standing Waves on a String v = = λ v 2l Harmonics f n = v n 2 l fn = nf 1

44 Multiple Harmonics can be present at the same time.

45 Which harmonics (modes) are present on the string? The Fundamental and third harmonic.

46 Strings & Atoms are Quantized The possible frequency and energy states of an electron in an atomic orbit or of a wave on a string are quantized. f = v n 2 l En = = nhf, n= 0,1,2,3, h 6.626x10 Js

47 Standing Waves in a Tube Open at both ends. v f = n n 2 L λ = 2L Resonant Frequencies: fn = nf 1 λ = L Same as a string fixed at both ends.

48 Standing Waves in a Tube Open at one end. λ = n 4L n odd f n = n odd v 4L

49 Standing Waves in a Tube What is the length of a tube open at both ends that has a fundamental frequency of 176Hz and a first overtone of 352 Hz if the speed of sound is 343m/s? v fn = n 2 L v L= n f 2 n m/ s = 2(176 Hz ) =.974m

50 Problem 33 Fig. P14.33, p.384

51 is a Longitudinal Wave

52 is a What you Hear The ear converts sound energy to mechanical energy to a nerve impulse which is transmitted to the brain. The Pressure Wave sets the Ear Drum into Vibration.

Drum to Stirrup: Simple Machine Amplification Since the pressure wave striking the large area of the eardrum is concentrated into the smaller area of the

53 Drum to Stirrup: Simple Machine Amplification Since the pressure wave striking the large area of the eardrum is concentrated into the smaller area of the stirrup, the force of the vibrating stirrup is nearly 15 times larger than that of the eardrum. This feature enhances our ability of hear the faintest of sounds.

Resonance of the Cilia Nerves The inner surface of the cochlea is lined with over 20 000 hair-like cilia connected to nerve cells, each differing in length by minuscule amounts.

54 Resonance of the Cilia Nerves The inner surface of the cochlea is lined with over hair-like cilia connected to nerve cells, each differing in length by minuscule amounts. Each hair cell has a natural sensitivity to a particular frequency of vibration. When the frequency of the sound wave matches the natural frequency of the nerve cell, that nerve cell will resonate with a larger amplitude of vibration which induces the cell to release an electrical impulse along the auditory nerve towards the brain.

55 Sound Generation Energy is transmitted as a pressure wave. There is no net motion of the medium. The medium oscillates in simple harmonic motion. The frequency of the wave is the same as the vibrating source. Vibrating String Spherically Symmetric Sound Source (bell).

56 Reflect ECHO

Echo vs Reverberation A reverberation is perceived when the reflected sound wave reaches your ear in less than 0.1 second after the original sound wave.

57 Echo vs Reverberation A reverberation is perceived when the reflected sound wave reaches your ear in less than 0.1 second after the original sound wave. Since the original sound wave is still held in memory, there is no time delay between the perception of the reflected sound wave and the original sound wave. The two sound waves tend to combine as one very prolonged sound wave.

$Diffract We can hear around corners. Why can t we see around corners?$

58 Diffract We can hear around corners. Why can t we see around corners? If the size of the wave (wavelength) is close in size to the object (door way) then the wave will diffract (bend).

59 Refract Sound waves refract (bend) when moving between mediums in which it travels at different speeds.

60 The intensity of a wave, the power per unit area, is the rate at which energy is being transported by the wave through a unit area A perpendicular to the direction of travel of the wave: I = P W 4π r m 2 2

61 I = P W 4π r m The power transmitted by a wave is proportional to the amplitude of the wave. 2 2

62 A bell produces sound energy at a rate of W and radiates it uniformly in all directions. What is the intensity of the wave 10 m from the bell? I Power = = Area P 4π r 2 I = 3 4.0x10 W 2 4 π (10 m) = 3.2x10 W / m 6 2

63 Cochlear Cilia Nerve Damage Excessive exposure to loud sound can damage your cilia. Normal Ear Damaged Ear

64 Threshold of hearing : I = 10 W / m 10 2 Whisper: I = 10 / W m 6 2 Normal Conversation: I = 10 W / m 4 2 Bursting of eardrums : I = 10 W / m 0 db 20 db 60 db 160 db I Whisper I 0 = 10 10decibels 1bel 2 I W log 2 I 0 = 2 bels = 20 decibels

65 Decibel Index: β 0 10 log I 12 2 Threshold of hearing : I = 10 W / m = db I0 Whisper: 20db Conversation: 60db Loud Music: 120 db Jet: 140 db Rocket: 250dB

67 OSHA Safety Standards OSHA - Occupational Safety and Health Act - The OSHA criteria document reevaluates and reaffirms the Recommended Exposure Limit (REL) for occupational noise exposure established by the National Institute for Occupational Safety and Health (NIOSH) in The REL is 85 decibels, A-weighted, as an 8-hr time-weighted average (85 dba as an 8-hr TWA). Exposures at or above this level are hazardous.

68 If a sound is twice as intense, how much greater is the sound level, in db? β 10dB log I 1 1 = I0 β 2 10 log I 2 = db I0 I 2 I 1 β2 β1 = 10dB log 10dB log I I 0 0 β β 10 I log I / = db I0 I0 10dB log I 2 = I1 = = 3.01dB β2 β1 10dB log 2 53 db is twice as intense as 50dB. Log Scale!!

69 The decibel level of a jackhammer is 130 db relative to the threshold of hearing. Determine the sound intensity produced by the jackhammer. β 130dB 10 log I 1 10 log I 1 = db I0 1 = db I0 I log 13 I 10 = = I I log I I = I = 10 I0 =10 10 = 10 W / m 2

70 I = P W 2 2 4π r m Intensity 10dB log I β = I0 A point source emits sound with a power output of 100 watts. What is the intensity (in W/m 2 ) at a distance of 10.0 m from the source? What is it in db?

71 I = You Try Calculate the intensity level in db of a sound wave that has an intensity of W/m 2. a. 20 b. 200 c. 92 d. 9 e. 10 P W 2 2 4π r m 10dB log I β = I0

72 I = P W 2 2 4π r m You Try 10dB log I β = I0 By what factor will an intensity change when the corresponding sound level increases by 3 db? a. 3 b. 0.5 c. 2 d. 4 e. 0.3

73 Loudness Perception: Phons Perception of Loudness depends on Frequency & Intensity

74 Sound Frequencies A middle C vibrates 252 times per second. Sonic: 20 Hz 20 khz INFRAsonic: f < 20Hz ULTRAsonic: f > 20kHz

75 Ultrasound:Pulverizing Tumors f I ~23kHz 5 2 ~10 W / m Deep Heat f I ~1MHz 3 2 ~10 W / m

76 Ultrasound Intensity of reflected sound wave (echo) is related to change in density in target. Ultrasound beam: 7MHz 1 mm detail I ~10-2 W

77 Weeks

"We do know in animal studies, certain levels of ultrasound can cause

78 "A Womb With a View" and "Fetal Fotos Peek in the Pod Hi Cost Hi-Definition Ultrasound Are there RISKS? "We do know in animal studies, certain levels of ultrasound can cause damages in growing bones, in developing bones," said Dr. Dan Schultz of the Food and Drug Administration.

79 Ultrasound Question How far apart are two layers of tissue that produce echoes having round-trip times that differ by 0.750μs? What minimum frequency must the ultrasound have to see detail this small? The speed of sound in human tissue is 1540m/s. v ( )( 1540 m s s) Δt 2 2 w 4 Δ = = = m d Δ d = d d = vt vt = v Δt/2 2 1 s 2 s 1 s v vw = fλ f = = λ 1540 ms m w 6 = Hz

80 Freaky Question Which travels further, high or low frequencies? Why? Low frequency waves travel further because high frequency waves are absorbed by molecules in the medium. All dat gets thru da wall is da boom boom Bass!

81 Animal Perception of Sound domestic cats ,000 Hz domestic dogs 40-46,000 Hz African 16-12,000 Hz elephants ,000 bats Hz rodents ,000 Hz Human: 20-20,00Hz

These infrasonic calls, with a frequency of about 21 Hz and a normal duration of 4-5 seconds, carry for long distances (several

82 Infrasonic Contact Calls Female African elephants use "contact calls" to communicate with other elephants in their bands (usually a family group). These infrasonic calls, with a frequency of about 21 Hz and a normal duration of 4-5 seconds, carry for long distances (several kilometers), and help elephants to determine the location of other Elephants. Calls vary among individual elephants, so that others respond differently to familiar calls than to unfamiliar calls. Perhaps elephants can recognize the identity of the caller.

Infrasonic: < 20Hz Scientists first detected infrasound in 1883, when the eruption of the Krakatoa volcano in Indonesia sent inaudible sound waves careening around the world, affecting barometric

83 Infrasonic: < 20Hz Scientists first detected infrasound in 1883, when the eruption of the Krakatoa volcano in Indonesia sent inaudible sound waves careening around the world, affecting barometric readings. The eruption of the Fuego volcano in Guatemala last year generated highamplitude infrasound, mostly below 10 hertz. The pressure readings show that the strength of these sound waves can reach the equivalent of 120 decibels.

The brain receives the sound waves in the form of nerve impulses.

84 Echolocation: Sonic Vision Dolphin Vocalization Dolphins produce high frequency (100kHz) clicks that pass through the melon. These sound waves bounce off objects in the water and return to the dolphin in the form of an echo. The brain receives the sound waves in the form of nerve impulses. By this complex system of echolocation, dolphins can determine size, shape, speed, distance, direction, and even some of the internal structure of objects in the water.

85 SOFAR Channel SOund Fixing And Ranging Acoustic Thermometry of Ocean Climate ATOC: 70 Hertz, with a sound pressure level of 195 db Dolphin, pinniped species sensitive to high frequencies (above 10,000 Hz) Baleen whales sensitive to low-frequencies (below 100 Hertz)

86 Low Frequency Active Sonar The LFAS system consists of a 35- ton block of 18 huge underwater speakers and dozens of microphones. The speakers emit a consistent low-frequency tone, between 100 and 500 Hertz, at 240dB, which travels out into the water at a depth of several hundred meters. The low frequency permits the sound to travel tremendous distances, detecting objects many hundreds of miles away by echolocation.

87 Physical Effect on Marine Life At a 1 mile radius from the ship the noise only dissipates to 180 db which causes a bubbling effect in marine mammals' blood stream which creates embolisms. At 100 mile radius from the ship the noise only drops to 160 db which causes shearing of the tissues in the air sack behind whales' and dolphins' brain. This air sack is highly sensitive since it is used in echolocation. This shearing of tissue then causes hemorrhaging in their brains. Fish have little hairs in their ears that transmit sound waves from their ear canals to their central nervous system. The 160 db level shears these hair right off. Granted they grow back in 2 weeks, but they are deaf and are more likely to be picked off by predators and can't find food. Any fish or marine mammals caught in this "death zone" would have to swim 100 miles to escape the noise and pain.

88 Novermber 28, 2004 Sound bombing" of ocean floors to test for oil and gas for National Security? More than 100 whales and dolphins died in two separate beachings in 24 hours on remote Australian islands

90 Deadly Sonar: NRDC

91 Gray whales migrating off the coast of Southern California

92 Sea Quakes produce powerful pressure waves that rupture the sinuses and middle ear of whales and dolphins.

93 Sound Weapons

$Atomic Blast Wave A fraction of a second after a nuclear explosion, the heat from the fireball causes a highpressure wave to develop and move outward producing the blast effect.$

94 Atomic Blast Wave A fraction of a second after a nuclear explosion, the heat from the fireball causes a highpressure wave to develop and move outward producing the blast effect. The front of the blast wave, i.e., the shock front, travels rapidly away from the fireball, a moving wall of highly compressed air. The blast wind may exceed several hundred km/h. The range for blast effects increases with the explosive yield of the weapon and also depends on the burst altitude.

96 Which is traveling at subsonic, sonic, or supersonic speeds? a) Subsonic b) Sonic c) Supersonic

99 RADAR: RAdio Detecting And Ranging

100 Cosmological Redshift: Expanding Universe Stellar Motions: Rotations and Radial Motions Solar Physics: Surface Studies and Rotations Gravitational Redshift: Black Holes & Lensing Extra-solar Planets via Doppler Wobbler

101

102 Case 1: Moving Source Stationary Observer v = 0 O v S Observer Reference Frame

103 Case 1: Moving Source Stationary Observer v = 0 O v S Observer Reference Frame

104 Case 1: Moving Source Stationary Observer v = 0 O v S Observer Reference Frame

105 Case 1: Moving Source Stationary Observer v = 0 O v S Observer Reference Frame

106 Case 1: Moving Source Stationary Observer v = 0 O v S Observer Reference Frame

107 Case 1: Moving Source Stationary Observer v = 0 O vwave = v What is the speed of sound to the observer? v =? S O Speed of a wave is determined by the properties of the Medium!

108 Case 1: Moving Source Stationary Observer v = 0 O vwave = v What is the speed of sound to the observer? S O v = v Speed of a wave is determined by the properties of the Medium!

109 Case 1: Moving Source Stationary Observer v = 0 O v = v λ < λ S O f > f

110 Case 1: Moving Source Stationary Observer v = 0 O v S source moves in time τ a distance v S τ

111 Case 1: Moving Source Stationary Observer v = 0 O v S emits another wavelength

112 Case 1: Moving Source Stationary Observer v = 0 O v S travels a distance vsτ and emits again...

113 Case 1: Moving Source Stationary Observer v = 0 O v S and so on...

114 Case 1: Moving Source Stationary Observer v = 0 O v S bunching up the wavecrests by v S τ

115 Case 1: Moving Source Stationary Observer v = 0 O λ is shortened by λ λ τ = v S v S v τ = λ(1 S ) λ v τ = λ(1 S ) vτ v v λ = λ( s ) v v = λ(1 S ) v

116 Case 1: Moving Source Stationary Observer v = 0 O f =? Use v = v v S v v λ λ v = s f λ ' = λ f = f = f λ f = f f λ λ v vs λ( ) v v v v S

117 Case 1: Source moving TOWARD (-) and AWAY (+) from Observer v v λ ± λ v = s v S f = f v v ± v S f = f 1 vs (1 ± ) v What if v = v? S

118 f = f 1 vs (1 ± ) v Source Moving: If v S f = = f v 1 vs (1 ± ) v = f 1 (1 1) = 1 0

119 f = f 1 vs (1 ) v v S = Mach # v If v S = v f = f 1 vs (1 ) v = f 1 (1 1) = 1 0

120

121

122 When the duck speed is equal or greater than the speed of waves in water, the waves form a bow wave.

123 Case 2: Observer Moving & Stationary Source Observer Moving TOWARD (+) and AWAY (-) from Source λ =? S v O v =? f =?

124 Case 2: Observer Moving & Stationary Source Observer Moving TOWARD (+) and AWAY (-) from Source λ = λ S v O f v = v± v o v± v = f o v f = f ± v v 0 (1 )

125 Doppler Shift Problem A siren, mounted on the tower, emits a sound with a frequency of 2140 Hz. What is the difference in the frequency heard by the driver travelling away from the tower at 27 m/s between the directed and reflected sound of the siren? Take the speed of sound to be 343 m/s. f = f(1 ± ) v v Direct (1 O v f = f ) f Reflected = f(1 + O ) v v v O Given : f = 2140 Hz, v= 343 m/ s, v = 27 m/ s O

126 Doppler Shift Problem v O f = f(1 ) Direct v Given : f = 2140 Hz, v= 343 m/ s, v = 27 m/ s O =1970Hz f f(1 ) Reflected v v O v O = + = 2310Hz f Direct = f(1 ) f Reflected = f(1 + ) v v v O

127 If both Source and Observer are moving.. Source Moving: 1 f = f vs (1 ± ) v f Observer Moving: = f ± v v 0 (1 ) v+ v f = f v v + : Moving Towards each other - : Moving Away from each other o s

is a What you Hear The Pressure Wave sets the Ear Drum into Vibration.

is a What you Hear The Pressure Wave sets the Ear Drum into Vibration. is a Pressure Wae is a What you Hear The ear conerts sound energy to mechanical energy to a nere impulse which is transmitted to the brain. The Pressure Wae sets the Ear Drum into Vibration. Drum to Stirrup: