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					Sound and the human ear
                  Sound
• Sound radiates from the point source in all
  directions
• Sound intensity is power / Area
• Spherical area is 4πr2 so sound intensity is
  power / 4πr2 Watts/m2
• Double r and intensity is quartered as
  intensity is proportional to 1/r2 (inverse
  square law)
• Humans are have very sensitive ears capable of
  detecting sound waves of extremely low intensity
• The faintest sound which the typical human ear
  can detect has an intensity of 1*10-12 W/m2
  (corresponds to a sound which will displace
  particles of air by a billionth of a centimetre).
  This is the “Threshold of hearing”
• Ear can cope with sound intensity 1 billion times
  greater than the threshold of hearing without
  damage
• A linear scale of sound intensity is obviously
  impractical
    Bels (Alexander Graham Bell)
•   0B equivalent to 1*10-12 W/m2
•   1B = 10 times intensity 1*10-11 W/m2
•   2B = 100 times -> 1*10-10 W/m2
•   4B = 1000 times -> 1*10-9 W/m2
•   5B = 10000 times -> 1*10-8 W/m2
•   6B= 100000 times -> 1*10-7 W/m2
•   Bel is considered too large and 0.1B change in
    intensity is just about noticeable so dB more
    convenient measure
                                             Intensity     Num of Times
          Source               Intensity
                                               Level     Greater Than TOH


Threshold of Hearing (TOH)   1*10-12 W/m2      0 dB            100

     Rustling Leaves         1*10-11 W/m2     10 dB            101

         Whisper             1*10-10 W/m2     20 dB            102

   Normal Conversation       1*10-6 W/m2      60 dB            106

    Busy Street Traffic      1*10-5 W/m2      70 dB            107

     Vacuum Cleaner          1*10-4 W/m2      80 dB            108

     Large Orchestra         6.3*10-3 W/m2    98 dB            109.8

Walkman at Maximum Level     1*10-2 W/m2      100 dB           1010

Front Rows of Rock Concert   1*10-1 W/m2      110 dB           1011

    Threshold of Pain         1*101 W/m2      130 dB           1013

    Military Jet Takeoff      1*102 W/m2      140 dB           1014

   Instant Perforation of
                              1*104 W/m2      160 dB           1016
            Eardrum
Threshold of hearing to 10,000,000,000,000 times TOH at threshold of pain
or 0db o 130 db

Intensity I = intensity/Intensity of TOH so dynamic range is:

1013/1 or in Bels, log10 1013 = 13 or in dBs 10 log10 1013 = 130dBs
• The ear is divided into 3 parts: outer, middle and inner ear
• pinna made of cartilage, directs sound into the auditory canal
   – Resonant freq ~ 3.5kHz (acoustic amplification)
   – sound vibrates the ear drum at the end of the canal
• Middle ear osscicles
• tympanic membrane (ear drum)
• ossicles (3 smallest bones)
   – Malleus (hammer)
   – Incus (anvil)
   – Stapes (stirrup)
   – matches low acoustic
     impedance of air to high
     acoustic impedance of
     fluid of inner ear
   – Pressure gain of about
     200
• Eustachian tube maintains
  pressure equilibrium
Built in protection for loud sounds. Muscles
tighten ear drum to reduce movement of osscicles
• Inner ear
   – Fluid filled
   – Semicircular canals for balance
   – Cochlea for sound perception
      • cochlea is coiled tube about 2 mm in diameter and 3 cm long




• Two openings from middle to outer:
   – oval and round windows
• 3 fluid-filled compartments:
  – scala vestibuli(2) ->Reissner’s membrane
  – scala media(1) -> basilar membrane
  – scala tympani(3)
• Cochlea rolled out
  – Two openings from middle to outer:
     • oval and round windows
• Cochlea rolled out
  – Two openings from middle to outer:
     • oval and round windows
     • HF Standing waves near oval window, LF furthest away
• Cochlea is a frequency spectrum analyser
   – Electrical impulses generated by the organ of corti which contains
     hundreds of thousands of hairs connected to nerves
   – Nerves bundled into the auditory nerve which connects to the
     brain
• The ear needs higher sound levels at low and high frequencies for
  equal loudness
• As sound intensity is frequency dependant, 60dB at one frequency
  is not the same as 60dB at another. 1kHz is used as a reference
  frequency and the intensity at this frequency is measured in phons.
  So 60dB sound at 1kHz is 60 phons
• Rule of thumb, 10 times the intensity sounds twice as loud
• Frequency response is non-linear
   – Mel(ody) = 1127.01048 x log_e(1+f/700)
   – f = 700(e^{m x 1127.01048} – 1)
   – Bark =13 x arctan(0.76f x 1000) + 3.5 x arctan((f x 7500)^2)