1. Intensity of Periodic Sound Waves 2. The Doppler Effect

Transcription

1 1. Intenity o Periodic Sound Wae. The Doppler Eect

2 Objectie: The tudent will be able to Deine the intenity o the ound wae. Deine the Doppler Eect. Undertand ome application on ound

3 3.3 Intenity o periodic wae: Conider an element o air o ma m and width x in ront o a piton ocillating with a requency, a hown in Fig. The piton tranmit energy to thi element o air in the tube, and the energy i propagated away rom the piton by the ound wae. To ealuate the rate o energy traner or the ound wae, we hall ealuate the kinetic energy o thi element o air, which i undergoing imple harmonic motion

4 Rate o Energy Traner by ound Wae: To ealuate the kinetic energy o thi element o air, we need to know it peed. ( x, t) S( x, t) max max t t The kinetic energy,dk, o the egment Dm i A Dx0, the energy DK become dk For the wae at t=0, the kinetic energy in one wae length, l, i K l S cokx-t -S inkx-t 1 AS 1 dk AS m 1 x DK m xl x0 1 in 1 4x in 4k l Dm 1 kxdx AS xl x0 1 Dm( -S max ) in kx-t 1 AS 4 m l m xl x0 1 co kx dx Jut like harmonic ocillation, the total mechanical energy in one wae length, l, i E l U l K l 1 S m Al

5 Rate o Energy Traner by ound Wae: A the ound wae moe through the air, thi amount o energy pae by a gien point during one period o ocillation. Hence, the rate o energy traner i El E P Dt T 1 A( l max 1 A( S ) max ) l T We deine the intenity I o a wae, or the power per unit area, to be the rate at which the energy being tranported by the wae traner through a unit area A perpendicular to the direction o trael o the wae: I P / A

6 Sound Leel in Decibel The human ear can detect i o wide, it wa conenient to ue a logarithmic cale, where the ound leel β (Greek beta) i deined by the equation: I o i the reerence intenity, taken to be at the threhold o hearing (I o = 1.00 x 10-1 W/m ), I i the intenity in watt per quare meter to which the ound leel β correpond, where β i meaured in decibel (db)

7 3.4 The Doppler Eect: I a point ource emit ound wae and the medium i uniorm, the wae moe at the ame peed in all direction radially away rom the ource; thi i a pherical wae. It i ueul to repreent thee wae with a erie o circular arc concentric with the ource, a in Fig, each arc repreent a urace oer which the phae o the wae i contant. For example, the urace could pa through the cret o all wae. We call uch a urace o contant phae a wae ront. The ditance between adjacent wae ront equal the waelength

8 1- When the oberer moe toward the ource, the peed o the wae relatie to the oberer i ` = o + a in the cae o the boat, but the waelength λ i unchanged. Hence, = λ, we can ay that the requency ` heard by the oberer i increaed and i gien by l l ' 0 Becaue λ= /, we can expre a 0 (oberer moing toward ource)

9 - When the oberer i moing away rom the ource, the peed o the wae relatie to the oberer i = - o. The requency heard by the oberer in thi cae i decreaed and i gien by l - - l 0 0 And λ= /, we can expre a (oberer moing away rom ource) In general, wheneer an oberer moe with a peed o relatie to a tationary ource, the requency heard by the oberer i gien by Equation, 0 with a ign conention: a poitie alue i ubtituted or o when the oberer moe toward the ource and a negatie alue i ubtituted when the oberer moe away rom the ource

10 When the ource moing:

11 3- When the ource moe directly toward oberer : The wae ront heard by the oberer are cloer together than they would be i the ource were not moing. A a reult, the waelength λ` meaured by oberer A i horter than the waelength λ o the ource. During each ibration, which lat or a time interal T (the period), the ource moe a ditance T = / and the waelength i hortened by thi amount. Thereore, the obered waelength λ` i l l - Dl l - / The requency ` heard by oberer A i l l - - / / - /

12 4- When the ource moe away rom a tationary oberer, a i the cae or oberer B in Fig, the oberer meaure a waelength λ` that i greater than λ and hear a decreaed requency: I both ource and oberer moe through the tranmitting medium, Where the upper ign (+ numerator, -denominator) correpond to the ource and oberer moing toward the other and the lower ign in the direction away rom the o other

13 Example 1: The iren o a police car emit a pure tone at a requency o 115 Hz. Find the requency that you would perceie in your car. (a) your car at ret, police car moing toward you at 9 m/; (b) police car at ret your moing toward it at 9 m/ (c) you and police car moing toward one another at 14.5 m/ (d) you moing at 9 m/, police car chaing behind you at 38 m/ The elocity o ound in air i 343 m/

14 Solution: Uing Here (b) c d 0 0 (a) ' - 0 9m / 343 ( m / ) 9 19Hz ' (115Hz) 10Hz m/ ' m / ' Hz Hz m /

15 Example A tationary ciil deene iren ha a requency o 1000 Hz. What requency will be heard by drier o car moing at 15 m/? A) away rom the iren? B) toward the iren? The elocity o ound in air i 344 m/

16 Solution: Moing away rom the iren d = - d = d = (1000 Hz) (344 m/ - 15 m/) 344 m/ d = 956 Hz Apparent requency heard by the detector decreae

17 Example 3 A police car with a 1000 Hz iren i moing at 15 m/. What requency i heard by a tationary litener when the police car i a) receding rom the detector? b) b) approaching the detector?

18 d = + d = (1000 Hz) 344 m/ = 958 Hz 344 m/ + 15 m/ P. car moing away d = - d = (1000 Hz) 344 m/ = 1046 Hz 344 m/ - 15 m/ P. car coming toward

19 The peed o ound The peed o ound in air i 343 meter per econd (660 mile per hour) at one atmophere o preure and room temperature (1 C). An object i ubonic when it i moing lower than ound

20 Shock Wae What happen when the peed o a ource exceed the wae peed. Thi ituation i depicted graphically in Figure. The circle repreent pherical wae ront emitted by the ource at ariou time during it motion. At t = 0, the ource i at S o, and at a later time t, the ource i at S n. At the time t, the wae ront centered at S o reache a radiu o t

21 Jet airplane traeling at uperonic peed produce hock wae, which are reponible or the loud onic boom one hear. The hock wae carrie a great deal o energy concentrated on the urace o the cone, with correpondingly great preure ariation. Such hock wae are unpleaant to hear and can caue damage to building when aircrat ly uperonically at low altitude. In act, an airplane lying at uperonic peed produce a double boom becaue two hock wae are ormed, one rom the noe o the plane and one rom the tail. People near the path o the pace huttle a it glide toward it landing point oten report hearing what ound like two ery cloely paced crack o thunder

22 The peed o ound We ue the term uperonic to decribe motion at peed ater than the peed o ound. A hock wae orm where the wae ront pile up. The preure change acro the hock wae i what caue a ery loud ound known a a onic boom

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