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Waves and Sound

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Title: Waves and Sound


1
Waves and Sound
2
Remember Periodic Motion?
  • Motion which repeats in a regular cycle
  • Pendulum, vibrating spring, vibrating guitar
    string

3
Simple Harmonic Motion
  • Motion around a point of equilibrium
  • Force proportional to displacement of object from
    equilibrium

4
What is a wave?
  • Wavedisturbance that carries energy through
    matter or space
  • Note that the actual matter does not travel far
    but the energy can- the energy in this wave could
    have traveled from Alaska!

5
Classification of Waves
  • Waves Are
  • Mechanical or Non-Mechanical
  • One (or More) Pulses or Periodic
  • Longitudinal or Transverse or Combined

6
Mechanical Waves
  • Require A Medium For Transmission
  • Medium Mass / Atoms / Material
  • Transmitted Via Vibration Of Particles In The
    Medium Around A Rest Position
  • Examples
  • Sound
  • Water Wave

7
Non-Mechanical Waves
  • No Medium Is Required For Transmission
  • Can Be Transmitted Through Empty Space
  • Examples
  • Visible Light
  • Infrared Or Ultraviolet Light
  • Radio/TV Waves Microwaves
  • Any Electromagnetic Radiation

8
Pulse vs. Periodic
  • Pulse
  • A Single Vibratory Disturbance
  • Periodic Wave
  • A Series Of Regular Disturbances
  • Regular Identical Evenly Timed

9
Transverse waves
  • Disturbance is perpendicular to the motion of the
    wave
  • http//www.youtube.com/watch?vcPKGa2DsIs0

10
Longitudinal Waves
  • Disturbance is parallel to motion of wave
  • Ex- sound waves
  • Fluids usually only transmit longitudinal waves

11
Surface Waves/Elliptical Waves
  • Underwater, waves are longitudinal but at the
    surface they have elements of both longitudinal
    and transverse
  • Motion of a particle on the surface is an ellipse

12
Torsional Waves
  • Twist around a central axis
  • Like Tacoma Narrows Bridge

13
Wave properties
  • Equilibrium
  • Crest
  • Trough
  • Amplitude
  • Phase
  • Wavelength

14
Amplitude
  • Maximum displacement of a particle in a wave from
    the equilibrium
  • Examples brightness of a light, loudness of a
    sound

15
Wavelength
  • Distance between 2 corresponding locations
  • Usually measured from crest to crest or trough to
    trough
  • Symbol is ?

16
Amplitude and Wavelength
  • These waves have the same wavelength but
    different amplitudes
  • These waves have the same amplitude but different
    wavelengths

17
Phase
  • Points On A Periodic Wave Are In Phase If They
    Have
  • Same Displacement From Rest Position
  • AND
  • Same Direction Of Motion
  • C and F are In Phase

18
Phase
  • Points that are in phase act the same- they are
    a whole multiple of a wave apart
  • Since wavelength is one complete cycle, we
    usually refer to it as 360?
  • So in phase n360
  • Points that are out of phase are not a whole
    multiple of 360? apart- they can be any of
    degrees apart
  • We usually look at 90?, 180?, and 270? apart

19
Phase Problems-
  • Using A as a reference, which point(s) are
  • 360? in phase
  • 90?out of phase
  • 180? out of phase
  • 270?out of phase

20
Frequency
  • Number of vibrations per second
  • Symbol is f
  • Unit is Hz (1/s)

21
Period
  • Time to complete one cycle
  • Symbol is T
  • Unit is s
  • T1/f

22
Speed
  • Speed of a wave wavelength x frequency
  • v ?f
  • Examples- we see the baseball hit the bat before
    we hear it b/c light wave travels faster than
    sound wave

23
Comparing Wave Speeds
  • Light 3.00 x 108 m/s
  • Sound 3.31 x 102 m/s
  • We See The Lightning Flash Before We Hear The
    Thunder.
  • We See The Bat Hit The Ball Before The Crack Is
    Heard

24
Speed of a Wave on a String
  • For faster waves tighter string (more tension)
    or lighter string (less mass per length)
  • Mass/length is known as the linear mass density

25
Speed of wave problems
  • A ball of string is purchased at a local hardware
    store. According to the manufacturer, the package
    contains 100 yards (91.5 meters) of string and
    has a mass of 12 oz (341 grams)
  • What is the string's linear mass density?
  • If the string's tensile strength is 90 N, what is
    the maximum speed a pulse could travel along the
    string?

26
solutions
  • Mass/length 3.73 x 10-3 kg/meter
  • Speed155.3 m/sec

27
Wave Graphs- same shape but different info
  • Vibration graph- shows behavior at one spot
  • Waveform graph shows wave behavior in many spots
    at one time

28
Problems
  • A periodic wave goes through twenty complete
    cycles of its motion in 4.0 seconds
  • What is the frequency of the wave?
  • What is its period?
  • Determine the frequency of a wave whose period is
    5.0 seconds

29
Wavefront
  • The Locus Of Adjacent Points Which Are In Phase
  • Such As The Crest Of A Water Wave

30
Spherical Wavefront
31
Spherical Wavefront
32
Periodic Wave Phenomena
  • Superposition/Interference
  • Resonance
  • Doppler Effect
  • Diffraction
  • Reflection
  • Refraction

33
Waves at An Interface
  • Interface
  • A Boundary With A Different Medium
  • Part Of The Wave Is Reflected
  • Part Is Transmitted Through The Second Medium
  • Part Is Absorbed (Turns Into Heat)
  • Speed can change

34
Reflection
  • At a rigid boundary, when wave hits with an
    upward force, the boundary medium will react with
    a downward force so reflected wave is
  • INVERTED
  • If boundary is nonrigid (it can move) wave will
    reflect in same orientation

35
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36
Refraction
  • When a wave enters a new medium velocity can
    change causing wave to bend

37
Doppler Effect
  • A Variation In Observed Frequency When There Is
    Relative Motion Between A Source And An Observer
  • Approaching
  • Higher Frequency Observed
  • Receding
  • Lower Frequency Observed
  • Sound
  • Pitch Changes
  • Light
  • Color Changes

38
Doppler Effect Examples
  • Siren Passing

39
Doppler Effect
40
Calculations involving Doppler Effect
  • Let fs be the source frequency and fd be the
    detected frequency
  • If source moving towards you, frequency will
    increase so choose or - accordingly
  • fd(vvd)/(vvs) fs
  • Thus, if moving away, frequency will be lower
  • If moving towards, frequency will be higher

41
Example Doppler
  • A car is traveling 20 m/s away from a stationary
    observer. If the cars horn emits a frequency of
    600Hz, what frequency will the observer hear?
  • Use v340m/s for the speed of sound

42
Solution
  • Since car is traveling away from observer,
    frequency will be lower
  • fd(3400)/(34020) 600Hz 567Hz

43
Breaking the sound barrier
  • Speed of sound varies in different mediums
  • When something travels faster than the local
    speed of sound it breaks the sound barrier

44
Breaking the sound barrier
Regions of constructive interferenceSHOCK WAVES
45
Superposition of waves
  • When 2 waves meet, the displacement in the medium
    is the sum of the individual displacements
  • They then continue, unchanged by their meeting

46
Constructive Interference
  • Maximum Constructive Interference Occurs When The
    Phase Difference Is 0 In Phase

47
Destructive Interference
  • Maximum Destructive Interference Occurs When The
    Phase Difference Is 180 Out of Phase

48
Interference Patterns
  • Symmetrical Patterns Produced By Sources In Phase
    In The Same Medium

49
Interference Can Produce Colors
50
Interference Patterns
51
Interference Patterns
  • Maximum destructive interference produces nodes
  • Maximum constructive interference produces
    anti-nodes
  • http//www.physicsclassroom.com/mmedia/waves/ipd.c
    fm

52
Nodes and Antinodes
  • Nodes-
  • net displacement0
  • Antinodes-
  • Net displacement max

53
Nodes Anti-Nodes
  • Nodes
  • Points of NO DISPLACEMENT
  • Anti-Nodes
  • Points of MAXIMUM DISPLACEMENT
  • Line of Nodes
  • Smooth Area

54
Standing Waves
  • Each object has a natural frequency at which it
    is willing to vibrate
  • If you force a vibration at this frequency,
    object will resonate or vibrate at increasing
    amplitude
  • Next shower, try to test this- sing different
    notes until you reach one that is significantly
    louder (increased amplitude)
  • We can make this using a wave reflecting off a
    boundary at the same frequency, amplitude, and
    wavelength

55
Resonance
  • If small, regular forces applied at just the
    right time it can increase the amplitude of
    vibration
  • Ex- trampoline, maybe Tacoma Narrows Bridge?
  • In a string, this depends on its length- always
    draw!
  • http//www.ngsir.netfirms.com/englishhtm/StatWave.
    htm

56
Nodes, Antinodes in Standing Waves
  • Nodes and antinodes alternate
  • Each node is 1/2? from the last
  • We use this to determine how standing waves form

57
Standing Waves
Notice there are distinct wavelengths that can
produce these standing waves. Note 1st
overtone2nd harmonic
2nd harmonic 3rd harmonic 4th harmonic
fundamental
58
Harmonics vs overtones
  • Lets take a guitar string the fundamental
    (also known as 1st harmonic) is when there is ?/2
    wavelengths

59
2nd harmonic (1st overtone)
  • The second harmonic occurs when you have twice
    the fundamental so 2(?/2)1 wavelength

60
3rd harmonic
  • Now we have 3x the fundamental or 3(?/2)3?/2 or
    1.5 wavelengths
  • Are we seeing the pattern here?
  • NOTEuse the term harmonic since it matches the
    math

61
Determining harmonic frequencies
  • Consider an 80-cm long guitar string that has a
    fundamental frequency (1st harmonic) of 400 Hz.
  • What is the wavelength of the 2nd harmonic?

62
  • wavelength is 160 cm or 1.60 m.
  • Now what is the speed of the wave?

63
  • speed frequency wavelength
  • speed 400 Hz 1.6 mspeed 640 m/s
  • Now, the speed of the other harmonics is the
    same- you can use their wavelengths to determine
    the frequency of each harmonic
  • What is the frequency of the 2nd harmonic?

64
solution
  • Wavelength of 2nd harmonic would be 0.8m
  • fv/?
  • f640/0.8800Hz
  • Now calculate frequency of 3rd harmonic

65
Standing waves- strings
  • Strings are fixed on both ends
  • How does the fundamental frequency compare to the
    length of the string?
  • Draw the fundamental and 2 harmonics

66
Resonance in Strings- Probs
  • Two identical vibrating strings are 2.0 meters
    long and uniform in density. One is fixed on both
    ends, the other is free on one end.
  • What is the wavelength of the fundamental
    frequency along the fixed-end string?
  • What is the wavelength of the fundamental
    frequency along the free-end string?
  • What is the wavelength of the first overtone
    along the free-end string?
  • What is the wavelength of the second overtone
    along the fixed-end string?

67
Resonance and Wave Speed
  • Now put it together with wave speed in a spring
  • Suppose a string of length 100 meters has a mass
    of 300 grams determine the fundamental frequency
    in this string when a 5-kg mass is suspended from
    a 1-meter vibrating section.

68
Sketch the problem
69
solution
  • T mg T (5)(9.81) 49.05 N
  • mass/length 0.3 / 100 3 x 10-3 kg/m
  • for the fundamental, L ½? 1 meter ? 2
    meters
  • vw v49.05/(3 x 10-3)
  • vw 127.8 m/sec
  • vw f?
  • 127.8 f(2)
  • f 63.9 hz

70
Free and Fixed End Reflectors
  • Free end reflector one end is fixed and one is
    free
  • Reflection is in phase (crest reflects as a
    crest)
  • http//www.physicsclassroom.com/mmedia/waves/fix.c
    fm
  • Fixed end reflector both ends fixed
  • Reflection is out of phase (crest reflects as a
    trough)
  • Try it )
  • http//www.physicsclassroom.com/mmedia/waves/free.
    cfm

71
Standing waves in sound- Closed Tube Sound waves
are longitudinal but we can draw them as
transverse to see them easily
  • In a closed tube, the far end is a node
    (particles cant compress)
  • The possible length of a tube follows a distinct
    pattern based on the fundamental being 1/4?
  • Note that only odd harmonics occur

72
Open-tube
  • Standing waves can still be established if the
    end is open- the waves reflect off the open air
  • In this case, the end is air which can vibrate so
    it is an antinode
  • Open tubes can support all harmonics

73
Harmonics and music
  • String instruments often have multiple harmonics
    vibrating simultaneously- this produces the
    particular timbre of the instrument
  • http//dev.physicslab.org/asp/applets/string/help.
    asp
  • The pentatonic scale- these overtones and
    fundamental
  • http//www.youtube.com/watch?vne6tB2KiZuk

74
Sound Waves
  • Mechanical
  • Need a medium
  • No sound in space

75
Sound Waves
  • Longitudinal
  • Vibrations create pressure variations in medium
  • Compressions
  • Rarefactions
  • Feel your throat as you hum
  • http//www.physicsclassroom.com/mmedia/waves/tfl.c
    fm

76
Visualizing a longitudinal wave
  • If you graph the difference in density/pressure
    in the medium, you can graph this as the
    amplitude and visualize it as a sinusoidal graph

77
Properties of sound waves
  • Share properties of waves
  • Speed v?f
  • Speed depends on medium and temperature
  • Reflection
  • Echo, sonar
  • Reflections of multiple or rough surfaces called
    reverberations
  • Interference
  • Dead spots(nodes)
  • amplification

78
Interference BEATS
  • Sound waves interfere just as other waves
  • If pitches of 2 waves are close, we hear
    resulting interference as beats- pulsating
    changes in amplitude (loudness)- the beats we
    hear are the areas of constructive interference

79
Beats Problems
  • Suppose you sound two tuning forks
    simultaneously one fork has a frequency of 256
    hz and the other has a frequency of 260 hz.
  • How many beats would be heard each second?
  • What is the pitch of these beats?

80
Beats
  • The frequency of the beats is the difference
    between the 2 original frequencies
  • beat frequency f2 - f1
  • The pitch of the beats is the average of the 2
    frequencies
  • beat pitch ½(f2f1)

81
Perception of Sound
  • Loudness amplitude
  • Measured in decibel (dB)
  • Exposure to loud sounds can cause your ear to
    lose sensitivity

82
Perception of Sound
  • Our perception of the loudness of a sound is not
    directly proportional to the pressure- intensity
    is actually logarithmic so for each 10 decibel
    increase, the intensity goes up 10X
  • Also depends on pitch, pure tone vs. combined
    tones

83
Speed of Sound
  • Depends on medium
  • Greater elasticity faster
  • Metals conduct sound quickly
  • Depends on temp
  • Hotfast
  • In same medium, all sound waves travel at same
    speed
  • When band plays- all sounds reach you at same
    speed regardless of pitch, amplitude, instrument

84
Speed of Sound in Air
  • In dry air, speed of sound is function of temp
  • vw 331 0.6 T
  • As air becomes more humid, speed increases
  • If air temp not constant, can cause refraction
  • When this happens with light, we see a mirage

85
Dampening
  • Sound waves cause vibrations in the medium so
    energy is lost to heat- thus the wave is damped
  • Lower frequency cause less motion so can travel
    farther- thus use low frequency for fog horns

86
Physics of Music
  • Sound produced by vibrating object which causes
    pressure oscillations in air
  • Vibrating string
  • Vibrating reed(s)
  • Vibrating column of air
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