Chapter 22B: Acoustics A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007
Objectives: After completing this module, you should be able to: Compute intensity and intensity levels of sounds and correlate with the distance to a source. Apply the Doppler effect to predict apparent changes in frequency due to relative velocities of a source and a listener.
Acoustics Defined Acoustics is is the branch of of science that deals with the physiological aspects of of sound. For example, in in a theater or or room, an engineer is is concerned with how clearly sounds can be heard or or transmitted.
Audible Sound Waves Sometimes it is useful to narrow the classification of sound to those that are audible (those that can be heard). The following definitions are used: Audible sound: Frequencies from 20 to 20,000 Hz. nfrasonic: Frequencies below the audible range. Ultrasonic: Frequencies above the audible range.
Comparison of Sensory Effects With Physical Measurements Sensory effects Physical property Loudness Pitch Quality ntensity Frequency Waveform Physical properties are measurable and repeatable.
Sound ntensity (Loudness) Sound intensity is is the power transferred by a sound wave per unit area normal to to the direction of of wave propagation. P A Units: W/m 2
sotropic Source of Sound An isotropic source propagates sound in ever-increasing spherical waves as shown. The ntensity is given by: P A P 4 r 2 ntensity decreases with the square of of the distance r from the isotropic sound source.
Comparison of Sound ntensities The inverse square relationship means a sound that is is twice as as far away is is one-fourth as as intense, and one that is is three times as as far away is is one-ninth as as intense. r 1 1 P P 1 2 4 r 2 2 1 4 r2 r 2 P 4r 4r 2 2 1 1 2 2 2 Constant Power P r r 2 2 11 2 2
Example 1: A horn blows with constant power. A child 8 m away hears a sound of intensity 0.600 W/m 2. What is the intensity heard by his mother 20 m away? What is the power of the source? Given: 1 = 0.60 W/m 2 ; r 1 = 8 m, r 2 = 20 m 2 2 2 r 11 r 1 r 11 r 2 2 or 2 2 1 r2 r2 2 2 2 8 m 0.60 W/m 20 m 2 2 = 0.096 W/m 2
Example 1: (Cont.) What is the power of the source? Assume isotropic propagation. Given: 1 = 0.60 W/m 2 ; r 1 = 8 m 2 = 0.0960 W/m 2 ; r 2 = 20 m P or P 4r 4 (8 m) (0.600 W/m ) 2 2 2 1 2 1 1 4 r1 P = 7.54 W The same result is found from: P 4 2 2 2 r
Range of ntensities The hearing threshold is the standard minimum of intensity for audible sound. ts value 0 is: Hearing threshold: 0 = 1 x 10-12 W/m 2 The pain threshold is the maximum intensity p that the average ear can record without feeling or pain. Pain threshold: p = 1 W/m 2
ntensity Level (Decibels) Due to the wide range of sound intensities (from 1 x 10-12 W/m 2 to 1 W/m 2 ) a logarithmic scale is defined as the intensity level in decibels: ntensity level 10log 0 decibels (db) where is the intensity level of a sound whose intensity is and 0 = 1 x 10-12 W/m 2.
Example 2: Find the intensity level of a sound whose intensity is 1 x 10-7 W/m 2. 10log 10log 1 x 10 W/m 1 x 10 W/m 0 5 10 log10 (10)(5) -7 2-12 2 ntensity level: = 50 db
ntensity Levels of Common Sounds. 20 db Leaves or 65 db whisper Normal conversation Subway 100 db 140-160 db Jet engines Hearing threshold: 0 db Pain threshold: 120 db
Comparison of Two Sounds Often two sounds are compared by intensity levels. But remember, intensity levels are logarithmic. A sound that is 100 times as intense as another is only 20 db larger! Source A 20 db, 1 x 10-10 W/m 2 Source B B = 100 A 40 db, 1 x 10-8 W/m 2
Difference in ntensity Levels Consider two sounds of intensity levels 1 and 2 10log ; 10log 1 2 1 2 0 0 2 1 10log 10log 10log log 2 1 2 1 0 0 0 0 / 2 0 2 2 1 10log 2 1 10log 1/ 0 1
Example 3: How much more intense is a 60 db sound than a 30 db sound? 2 1 2 10log 1 2 2 60 db 30 db 10log and log 3 Recall definition: 10 2 2 3 log 3; 10 ; 1 1 1 1 log means 10 x N x N 2 = 1000 1
nterference and Beats f f f f + = Beat frequency = f -f
The Doppler Effect The Doppler effect refers to the apparent change in frequency of a sound when there is relative motion of the source and listener. v Sound source moving with v f s Left person hears lower f due to longer Right person hears a higher f due to shorter Apparent f 0 is affected by motion.
General Formula for Doppler Effect f V v 0 0 fs V vs Speeds are reckoned as positive for approach and negative for recession Definition of terms: f 0 = observed frequency f s = frequency of source V = velocity of sound v 0 = velocity of observer v s = velocity of source
Example 4: A boy on a bicycle moves north at 10 m/s.. Following the boy is a truck traveling north at 30 m/s.. The truck s s horn blows at a frequency of 500 Hz.. What is the apparent frequency heard by the boy? Assume sound travels at 340 m/s. 30 m/s 10 m/s f s = 500 Hz V = 340 m/s The truck is approaching; the boy is fleeing. Thus: v s s = +30 m/s v 0 = -10 m/s
Example 4 (Cont.): Apply Doppler equation. v s = 30 m/s f s = 500 Hz V = 340 m/s v 0 = -10 m/s f 0 f s V v 0 340 m/s ( 10 m/s) 500 Hz V v s 340 m/s - (30 m/s) f 0 330 m/s 500 Hz 310 m/s) ff 0 = 532 Hz
Summary of Acoustics Acoustics is is the branch of of science that deals with the physiological aspects of of sound. For example, in in a theater or or room, an engineer is is concerned with how clearly sounds can be heard or or transmitted. Audible sound: Frequencies from 20 to 20,000 Hz. nfrasonic: Frequencies below the audible range. Ultrasonic: Frequencies above the audible range.
Summary (Continued) Measurable physical properties that determine the sensory effects of individual sounds Sensory effects Physical property Loudness Pitch Quality ntensity Frequency Waveform
Summary (Cont.) Sound intensity is is the power transferred by a sound wave per unit area normal to to the direction of of wave propagation. P A Units: W/m 2
Summary (Cont.) The inverse square relationship means a sound that is is twice as as far away is is one-fourth as as intense, and one that is is three times as as far away is is one-ninth as as intense. P A P 4 r 2 r r 2 2 11 2 2
Summary of Formulas: P A 10log 0 2 1 10log 1 2 Hearing threshold: 0 = 1 x 10-12 -12 W/m 2 Pain threshold: p = 1 W/m 2 v = f f Beat freq. = f -f f V v 0 0 fs V vs
CONCLUSON: Chapter 22B Acoustics