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test

• Physics 202
• Professor Lee Carkner
• Lecture 10

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Announcement

• Tuesday help session moved to SC120 (physics
  discussion room)
• Practice problems on WebAssign and web page
• Test Friday
• ½ conceptual multiple choice
• ½ problems
• Equations given, but not labeled or explained
• Bring calculator and pencil

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PAL 9 Sound

• Changing medium to get max v
• v (B/r)½
• Want large B and small r
• A low density fluid that is hard to compress
• Changing medium to get max Dpm
• Dpm vrwsm (B/r)½rwsm B½r½wsm
• Large v and large r
• Want to increase v by increasing B, not
  decreasing r
• Want medium with large B and large r
• Such a fluid would be hard to move
• Heavy and hard to compress

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PAL 9 Sound (cont.)

• Interference from two loudspeakers
• To get destructive interference you want the
  received waves to be out of phase by ½ wavelength
  
• Want the difference in path length to be ½ l
• f 1150 Hz, v 343 m/s (for room temperature
  air)
• v lf, l v/f 343/1150 0.3 m
• Want DL to be 0.15 m
• If L1 is 4m, make L2 4.15 m
• Constructive interference occurs when DL 0l,
  1l, 2l
• L2 4 m (or 4.3 m or 3.7 m etc.)

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Intensity of Sound

• The loudness of sound depends on its intensity,
  which is the power the wave delivers per unit
  area
• I P/A
• The units of intensity are W/m2
• The intensity can be expressed as
• I ½rvw2sm2
• Compare to expression for power in a transverse
  wave
• Depends directly on r and v (medium properties)
• Depends on the square of the amplitude and the
  frequency (wave properties)

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Intensity and Distance

• Consider a source that produces a sound of
  initial power Ps
• As you get further away from the source the
  intensity decreases because the area over which
  the power is distributed increases
• The total area over which the power is
  distributed depends on the distance from the
  source, r
• I P/A Ps/(4pr2)
• Sounds get fainter as you get further away
  because the energy is spread out over a larger
  area
• I falls off as 1/r2 (inverse square law)

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Inverse Square Law
Source
r
A14pr2 I1 Ps/A1
2r
A24p(2r)2 16pr2 4A1 I2 Ps/A2 ¼ I1
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The Decibel Scale

• The human ear is sensitive to sounds over a wide
  range of intensities (12 orders of magnitude)
• To conveniently handle such a large range a
  logarithmic scale is used known as the decibel
  scale
• b (10 dB) log (I/I0)
• I0 10-12 W/m2 (at the threshold of human
  hearing)
• log is base 10 log (not natural log, ln)
• There is an increase of 10 dB for every factor of
  10 increase in intensity

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Sound Levels

• Hearing Threshold
• 0 dB
• Whisper
• 10 dB
• Talking
• 60 dB

• Rock Concert
• 110 dB
• Pain
• 120 dB

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Music

• A musical instrument is a device for setting up
  standing waves of known frequency
• A standing wave oscillates with large amplitude
  and so is loud
• We shall consider an generalized instrument
  consisting of a pipe which may be open at one or
  both ends
• Like a pipe organ or a saxophone
• There will always be a node at the closed end and
  an anti-node at the open end
• Can have other nodes or antinodes in between, but
  this rule must be followed
• Closed end is like a tied end of string, open end
  is like a string end fixed to a freely moving ring

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Sound Waves in a Tube
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Harmonics

• Pipe open at both ends
• For resonance need a integer number of ½
  wavelengths to fit in the pipe
• Antinode at both ends
• L ½ l n v lf
• f nv/2L
• n 1,2,3,4
• Pipe open at one end
• For resonance need an integer number of ¼
  wavelengths to fit in the pipe
• Node at one end, antinode at other
• L ¼l n v lf
• f nv/4L
• n 1,3,5,7 (only have odd harmonics)

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Harmonics in Closed and Open Tubes
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Musical Instruments

• When playing a musical instrument you change n, v
  or L to produce a sound at the desired frequency
• Musical notes are related to a specific frequency
  
• For example A 440 Hz
• Music is the superposition of all of the notes
  being played at one time
• Smaller instruments generally produce high
  frequency sound
• f is inversely proportional to L

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Beat Frequency

• You generally cannot tell the difference between
  2 sounds of similar frequency
• If you listen to them simultaneously you hear
  variations in the sound at a frequency equal to
  the difference in frequency of the original two
  sounds called beats
• fbeat f1 f2

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Beats
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Beats and Tuning

• The beat phenomenon can be used to tune
  instruments
• Compare the instrument to a standard frequency
  and adjust so that the frequency of the beats
  decrease and then disappear
• Orchestras generally tune from A (440 Hz)
  acquired from the lead oboe or a tuning fork