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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 Source Intensity Intensity Level Num of Times 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 Eardrum 1*104 W/m2 160 dB 1016 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)