14.1) Producing a Sound Wave

  compression or condensation - region of high pressure
  
  rarefaction - region of low pressure
  
  A sound wave is a pattern of compression followed be rarefaction of air
  
14.2) Characteristics of Sound Waves

  The motion of the medium particles in a longitudinal sound wave is back and
  forth along the direction in which the wave travels.
  
  In a transverse wave, the particles move perpendicular to the direction in 
  which the wave travels.
  
  Categories of Sound Waves
  
  Audible waves: lie within the range of sensitivity of the human ear.
  approximately 20 Hz to 20000 Hz.
  
  Infrasonic waves: Below the audible range.
  
  Ultrasonic waves: Above the audible range.
  
  Applications of Ultrasound: similar to an X-ray but less harmful.  Used to
  take pictures of babies before they are born.
  
14.3) The speed of sound.

  The speed of sound in a liquid or gas.

  v = sqrt(B/ρ)
  
  where B is the bulk modulus and ρ is the equilibrium density.
  
  The speed of sound in a solid rod.
  
  v = sqrt(Y/ρ) 
  
  where Y is the Young's modulus of the solid and ρ is the density of the
  solid.
  
14.4) Energy and Intensity of Sound Waves

  The intensity, I, of a wave is the rate at which energy flows through a unit 
  area, A, perpendicularly to the direction of travel of the wave.

         
  I ≡  ΔE   = power
      A Δt    area
  
  Intensity Levels in Decibels
  
  β = 10 log(I/Io)
  
  where the constant Io is the reference intensity.
  
14.5) Spherical and Plan Waves
                        _
  I = average power =   P 
         area          4πr2
		 
14.6) Doppler Effect

  The Doppler Effect is experienced when there is a relative motion between the 
  source of the sound waves and the observer.  If the relative motion is towards
  each other, the observer detects an increase in pitch.  If the relative motion
  is away from each other, the observer detects a decrease in pitch.
  
  f' = f((v ± vo)/v)
  
  where vo is the velocity of the observer, f is the true frequency
  of the soundwave, v is the speed of sound, and f' is the detected frequency
  of the soundwave.
  
  In this equation, the positive sign is used when the observer is moving away
  from the source, and the negative sign is used when the observer is moving
  towards the source.
  
  f' = f( v /(v ± vs))
  
  Where vs is the velocity of the source.
  
  Combining these two equations:
  
  f' = f((v ± vo)/(v ± vs))
   
  Talk about shock waves and the 'sonic boom' phenomenon.
  
14.7) Interference of Sound Waves

14.8) Standing Waves
  
  Standing Wave - a wave that appears to not move forward or backward
  
  node - a point in the wave that does not oscillate
  
  antinode - where the wave vibrates with largest amplitude
  
  dNN = 1/2  λ
  
  The distance between two nodes in a wave is 1/2 of the wavelength.
  
  f1 = 1/(2L) * sqrt(F/μ)
  
  where L is the length of the string, F is the tension in the string, and μ
  is the mass per unit length of the string.
  
  The characteristic frequencies (produce standing waves) are given by
  
  fn = nf1 = n/(2L) * sqrt(F/μ)
  
  1f1 is called the first harmonic.
  
  2f1 is called the second harmonic.
  
14.9) Forced Vibrations and Resonance

  forced vibration - material is pushed back and forth forcing it to vibrate
  
  resonant frequency - the frequency at which the reflected waves become 
  maximally constructive
  
  resonance - an object that has reached a resonant frequency is said to be in
  resonance
  
14.10) Standing Waves in Air Columns
  
    If a pipe is open at both ends, all harmonics are present
	
	fn=n v/(2 L)
	
	If a pipe is closed at one end, only odd harmonies are present
	
	fn=n v/(4 L)
  
  
  
  
HW 6:
p. 476 # 1, 13 
p. 477 # 17
p. 478 # 29, 36