# Fourier series

Document Sample

```					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
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)

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 3 posted: 3/28/2011 language: English pages: 18
How are you planning on using Docstoc?