Sound and the human ear

Sound Sound radiates from the point source in all directions Sound intensity is power / Area Spherical area is 4πr 2 so sound intensity is power / 4πr 2 Watts/m 2 Double r and intensity is quartered as intensity is proportional to 1/r 2 (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* W/m 2 (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* W/m 2 1B = 10 times intensity 1* W/m 2 2B = 100 times -> 1* W/m 2 4B = 1000 times -> 1*10 -9 W/m 2 5B = times -> 1*10 -8 W/m 2 6B= times -> 1*10 -7 W/m 2 Bel is considered too large and 0.1B change in intensity is just about noticeable so dB more convenient measure

SourceIntensity Level Num of Times Greater Than TOH Threshold of Hearing (TOH)1* W/m 2 0 dB10 0 Rustling Leaves1* W/m 2 10 dB10 1 Whisper1* W/m 2 20 dB10 2 Normal Conversation1*10 -6 W/m 2 60 dB10 6 Busy Street Traffic1*10 -5 W/m 2 70 dB10 7 Vacuum Cleaner1*10 -4 W/m 2 80 dB10 8 Large Orchestra6.3*10 -3 W/m 2 98 dB Walkman at Maximum Level1*10 -2 W/m dB10 Front Rows of Rock Concert1*10 -1 W/m dB10 11 Threshold of Pain1*10 1 W/m dB10 13 Military Jet Takeoff1*10 2 W/m dB10 14 Instant Perforation of Eardrum 1*10 4 W/m dB10 16

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: /1 or in Bels, log = 13 or in dBs 10 log = 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) = x log_e(1+f/700) –f = 700(e^{m x } – 1) –Bark =13 x arctan(0.76f x 1000) x arctan((f x 7500)^2)