Introduction to Audio and Music Engineering
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1 Introduction to Audio and Music Engineering Lecture 7 Sound waves Sound localization Sound pressure level Range of human hearing Sound intensity and power 3
2 Waves in Space and Time Period: T Seconds Frequency: f = 1 /T Hertz (cycles per second) Angular Frequency: ω = 2π f Radians per second Spatial Wavelength: Spatial Wavenumber: λ k = 2π / λ Meters Radians per meter On a string the frequency of oscillation and the wavelength are connected through the speed of propagation of a bending wave. f λ = c = ω k c λ
3 Sound waves Sound is a Longitudinal Wave: Disturbance varies along the direction of propagation. Transverse wave: (string) Disturbance varies in a direction perpendicular to the direction of propagation. Density of air = 1.21 kg/m 3 pressure c = 343 m/sec λ = c / f λ f 20 Hz à 20 khz 5
4 Question What is the wavelength of a sound wave of frequency 20 Hz? c = 343 m/sec meters Wavelength = khz 20 Hz f 20 khz 17 m λ 1.7 cm c = 343 m/sec = 1125 ft/sec à about 1 foot per millisecond Remember this! 6
5 Speed of sound in air vs Temperature 360 Speed (m/sec) Temp Measured Measured Formula c = *T( C) Temperature C 7
6 Speed of Sound in Various Gases Gas Temperature ( C) Speed in m/s Air Air Hydrogen Carbon Dioxide Helium Sulfur Hexaflouride Water Vapor hops:// hops:// 8
7 Why does your voice sound different in different gases? SF 6 He c = f λ f = c λ Wavelength is fixed by size of vocal tract but c changes so the resonant frequencies of the vocal tract change 9
8 Human ability to localize sound Distance between human ears is cm λ f = c / λ f 1430 Hz 10
9 Sound localization f < 1500 Hz Wavelength of sound is larger than distance between ears f > 1500 Hz Wavelength of sound is smaller than distance between ears Humans determine directionality of sound by two basic methods: Interaural Time Difference (ITD) f < 1500 Hz Interaural Intensity Difference (IID) f > 1500 Hz But there is some overlap of methods in the range 800:1600 Hz 11
10 IID and ITD IID: f 1500 Hz ITD time delay: 22 cm à 650 µsec ITD: f 1500 Hz The shape of the outer ear (pinna) plays a significant role in 3D audio; Head Related Transfer Function: HRTF Head shadows the sound at more distant ear. 12
11 Stereo sound reproduction IID and ITD of the original source as heard by a listener are captured by the microphones. 13
12 Stereo sound reproduction Phantom source Stereo speakers attempt to reproduce the IID and ITD of the original source. 14
13 Sound Pressure Level SPL = 20log 10 P P ref P is the measured pressure P ref = 20 µpa (micro-pascals) 1 Pascal = 1 Newton/meter 2 Sound pressure of 20 µpa à 0 db SPL Sound pressure of 20 Pa à 120 db SPL 1 Atmosphere = 14.7 lbs/in 2 = 1.01 x 10 5 Pascals 1 Atmosphere = 194 db SPL 15
14 Range of Human Hearing HOG 143 db 16
15 Adaptation of Human Hearing At any given time we hear over a dynamic range of about 90 db. Our auditory system adapts our hearing sensitivity to the average SPL much like our eye adjusts to different lighting conditions. 90 db 0 db SPL 140 db SPL 17
16 Sound Intensity and Power Sound Intensity: When a pressure wave propagates through air the air moves slightly. p u I = p x u Nt m m 2 sec Dimensional Analysis = Nt m sec 1 m = energy 2 sec 1 area = power area Density of air u = p ρc Speed of sound ρc Impedance of air Small à air moves a lot Large à air moves little So I = p 2 ρc Sound Intensity Pressure 2 18
17 Inverse Square Law Power = I x 4πr 2 I = Power / 4πr 2 pop r I 2 = r 1 I 1 r 2 2 Total Radiated Sound Power of Musical Instruments Entire Orchestra 75 Watts Trombone 6 watts Violin 0.1 W 19
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