College Physics II Physics 1402 Fifth Class

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College Physics II - Physics 1402Fifth Class

• Some other Interference Ideas
• Sound Waves
• Human Range of Hearing
• Standing Waves or Resonance
• Intensity of Sound Waves
• Applications
• Beats
• Doppler Effect
• Music
• Lab Activity

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Harmonics for a String Fixed at One End and Free
at the Other

• Fundamental Harmonic - First Harmonic
• Third Harmonic - First Overtone
• Fifth Harmonic - Second Overtone
• Nodes and Antinodes Segments
• Frequencies and Wavelengths

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Sound Waves

• Wave Velocity for a Sound Wave
• Sound Velocities
• Examples
• Wave Function for a Sound Wave
• s (x,t) smax cos (kx - wt f) (in m)
• as a pressure wave
• DP Dpmax sin (kx - wt f) (in kPa)
• Energy E .5 (r A Dx) (w sm)2 (in J)
• Power P .5 (r A v) (w sm)2 (in W)

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Handout of Appendix I

• Derivation for the wave velocity of a traveling
  wave on a stretched string
• Derivation for the wave velocity of a traveling
  sound wave
• Wave Equation
• D - later

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Sound Waves

• Range of Hearing
• For Humans, 20 Hz to 20,000 Hz
• Low frequencies - high frequencies
• Infrasoncis - sounds below 20 Hz
• Ultrasonics - sounds above 20 kHz
• Examples
• Atmospheric Pressure
• 1.013 x 105 Pa (N/m2)
• 14.7 lb/in2
• 76 cm of Hg or 29.9 in of Hg

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Harmonics for a Pipe Opened at Both Ends (or
Closed at Both Ends)

• Fundamental Harmonic - First Harmonic
• Second Harmonic - First Overtone
• Nodes and Antinodes Segments
• Frequencies and Wavelengths

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Harmonics for a Pipe Opened at One End, Closed at
the Other

• Fundamental Harmonic - First Harmonic
• Third Harmonic - First Overtone
• Nodes and Antinodes Segments
• Frequencies and Wavelengths
• Examples
• Other Standing Waves

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Sound Intensity

• Intensity
• I P/A
• I .5 (r v) (w sm)2
• Threshold of Hearing - Io 1 x 10-12 W/m2
• Threshold of Pain - I 1 W/m2
• Decibel scale
• b 10 log (I / Io)
• Source of Sound b (dB) I (W/m2)
• Jackhammer 130 10
• Siren rock concert 120 1
• Busy traffic 80 1 x 10-3
• Normal conversation 50 1 x 10-7
• Whisper 30 1 x 10-9
• Rustling Leaves 10 1 x 10-11
• Threshold of Hearing 0 1 x 10-12

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Beats

• The periodic variation in intensity at a given
  point due to the superposition of two waves
  having slightly different frequencies.
• Df f2 - f1
• Interference of
• y1 A cos (2pf1t) and
• y2 A cos (2pf2t)
• y y1y2 2A cos2pt(f1-f2)/2cos2pt(f1-f2)/2

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Doppler Effect

• A shift in the frequency of the sound due to
  relative motion between the source and observer
• v is the velocity of sound in air fo is the
  original frequency with no object moving and lo
  is the original wavelength
• lo
• fo v
• v lofo ? fo v / lo

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Doppler Effect - Observer Moving Toward Source

• v v vo
• f v / lo ? f fo (1 v / vo)
• vo

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Doppler Effect - Observer Moving Away from Source

• v v - vo
• f v / lo ? f fo (1 - v / vo)
• vo
• V

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Doppler Effect - Source Moving Toward Observer

• l lo - vs / fo
• f v / l fo / (1 - vs / v)
• vs v

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Doppler Effect - Source Moving Away From Observer

• l lo vs / fo
• f v / l fo / (1 vs / v)
• v vs

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Combined Doppler Effect

• For original frequency, fo, and wave speed, v
• For vo, speed of observer, and vs, speed of
  source

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Music Expressions

• Pitch of a sound
• Similar to frequency of the sound wave
• Loudness of a sound
• Similar to the amplitude or intensity of the
  sound
• Quality of a Sound
• Similar to the overtone structure of the sound
• Musical Scales
• Just major scale - do-re-mi-fa-sol-la-ti-do
• Equal-tempered scale - piano scale

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Equal-Tempered Scale
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Next Class

• Applications, including
• Musical Instruments
• Human Ear
• Introduction to Optics
• Standing Waves Lab