Physics of Music Lecture 2: Waves and Sound - PowerPoint PPT Presentation

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Physics of Music Lecture 2: Waves and Sound

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X(t), V(t), A(t), V vs X. Torsion Wave Machine. PVC version on Quincke's Tube ... Waves diffract around obstacles. 03 Sept 2002. Physics of Music. 13 ... – PowerPoint PPT presentation

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Title: Physics of Music Lecture 2: Waves and Sound


1
Physics of MusicLecture 2 Waves and Sound
  • Phys 332W
  • Prof. Charles E. Hyde-Wright

2
Demonstrations
  • Mass on spring w/ PASCO
  • X(t), V(t), A(t), V vs X
  • Torsion Wave Machine
  • PVC version on Quinckes Tube
  • Speaker w/ and w/out baffle

3
Good Waves and Bad Waves
  • Fig 1-22 Bad cartoon (Infinite velocity)
  • Fig 1-23 Good wave (finite maximum velocity).

4
Why do things wiggle?--Inertia
  • Mass on a spring, child on a swing.
  • At the equilibrium point, the net force is
    zeroyet the motion continues (in fact the
    equilibrium point is the point of maximum
    velocity).
  • Force equals mass times acceleration
  • Acceleration is the rate of change of velocity
  • When the Force goes to zero, the velocity doesnt
    go to zero, the velocity stops changingthe
    object keeps going at the same speed.
  • See graphs with PASCO

5
Basic Wave Phenomena
  • Inverse Square Law
  • Polarization
  • Superposition
  • Constructive and Destructive Interference
  • Huygens Principle
  • Reflection
  • Refraction
  • Diffraction

6
Inverse Square Law
  • The energy density stored in a wave is
    proportional to the square of the wave amplitude
    (Intensity).
  • As a wave pulse travels outwards from a source,
    the total energy is conserved (ignoring
    dissipation to heat).
  • Since surface area grows as the square of
    distance, the amplitude of a FREELY expanding
    wave decreases linearly with distance, the
    intensity decreases with the square of distance.
  • If the wave is confined to a tube, the surface
    area remains constant with distance, the wave
    intensity remains constant

7
Inverse Square Law
  • Surface of Area expands as square of distance
    from source
  • Intensity decreases as one over radius squared.

8
Polarization
  • Sound is longitudinally polarized.
  • Surface water waves combine longitudinal and
    transverse polarization
  • Light is a transverse wave.
  • Electric and magnetic fields are the capability
    of exerting electromagnetic forces on charges in
    the path of the wave.
  • Matter waves electron, atom, are polarized with
    respect to the spin of the particle

9
Superposition (Physics)
  • Sound
  • You can hear and understand my voice, even if
    music is playing in the background.
  • The total sound wave reaching your ear is just
    the simple sum of voice music
  • Light
  • Your ability to see me is unaffected by the
    presence of other light waves bouncing around the
    room.

10
Superposition (Perception)
  • Two or more tones (especially in harmonic ratio)
    will blend into a single sound, retaining the
    pitch of the fundamental
  • Two light waves of different color (e.g. yellow
    and blue) will blend to form a new color, (green)
    even if no green light is present. Red and blue
    combine to form a color that does not correspond
    to any unique wavelength of light.
  • Constructive Interference

11
Superposition (Mathematics)
12
Huygens Principle
  • Each point on a wave acts as a source of a wave
    traveling outwards (in 3-dimensions, with 1/r2
    intensity).
  • The initial phase of the outward wave equals the
    phase of the source point.
  • The total wave amplitude at any point is equal to
    the sum of all waves coming from all the source
    points on the earlier wave.
  • Waves diffract around obstacles

13
Constructive and Destructive Interference
  • Two identical sources, in phase, combined to
    produce a sound intensity of 4 times either
    source by itself
  • Two identical sources, 180 degrees out of phase,
    combine to exactly cancel each other.
  • In this case, removing one source increases the
    sound level.

14
Refraction
15
Thermal Inversion Refraction
  • Thermal inversion (e.g. night time). Air is
    cooler near ground

16
Thermal Gradient Refraction
  • Usually, the air nearest the ground is hottest.
    This creates an upward refraction of sound

17
Wind Shear Refraction
  • Wind shear creates a focussing of sound downwind,
    a defocussing upwind

18
Beats
  • Combination of two tones.
  • File Beats.wav contains two pitches in ratios
    1001/1000, 1002/1000, 1004/1000, 1016/1000,
    1032/1000, 1064/1000, 1128/1000.
  • A musical half-step is a ratio 1059/1000

19
Doppler (Phys332W 2000 project,
www.physics.odu.edu/hyde/chw.htm)
20
Ultrasound
  • Frequency gt 20 KHz
  • Medical imaging uses simultaneous phase and
    intensity measurement with an array of
    piezo-electric transducers.
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