Physics 231 Lecture 28

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Marjory Greene
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1 Physics 31 Lecture 8 Cocepts or today s lecture Spherical waes P I 4πr Dopper shit + o ƒ' ƒ s Itererece o soud waes L L λ costructi e ( 0,1,) L 1 1 L ( + 1/ ) λ destructi e Stadig waes o strig: L λ L 1,,3,,,

2 Itesity o spherical waes. I oe suspeds o-directioal i soud source with power P i air, the soud will radiate i all directios. All poits o a sphere o radius r will see the same soud itesity IP/A: I P 4πr r Fig 14.4, p. 433 Slide 8

3 Example Whe a helicopter is hoerig 1100 m directly oerhead, a obserer o the groud measures a soud itesity I 1. Assume that soud is radiated uiormly as a spherical wae rom the helicopter ad that groud relectios are egligible. How ar must the helicopter ly i a straight lie parallel to the groud beore the obserer measures a soud itesity o I I 1 /5? z y x r d h I I I 1 1/5 P P I 4 π r 1 4π r1 r h + d 5r 1 5h d 4h d h 00m

additioal umber o wae rots The requecy heard is icreased, the pitch is higher ƒ' + ƒ o A obserer

4 Doppler eect or moig obserer Fig 14.8, p. 435 Slide 1 Fig 14.9, p. 436 Slide 13 A obserer is moig toward a statioary source Due to his moemet, the obserer detects a additioal umber o wae rots The requecy heard is icreased, the pitch is higher ƒ' + ƒ o A obserer is moig away rom a statioary source The obserer detects ewer wae rots per secod The requecy heard is decrease, the pitch is lower

Doppler Eect, Source i Motio geeral ormula ƒ' + ƒ o s Both the source ad the obserer could be moig As the source moes toward the obserer (A), the waelegth appears shorter ad the requecy icreases As

5 Doppler Eect, Source i Motio geeral ormula ƒ' + ƒ o s Both the source ad the obserer could be moig As the source moes toward the obserer (A), the waelegth appears shorter ad the requecy icreases As the source moes away rom the obserer (B), the waelegth appears loger ad the requecy appears to be lower Use positie alues o o ad s whe the motio is toward Frequecy appears higher Use egatie alues o o ad s whe the motio is away Frequecy appears lower

6 Example A trai at rest emits a soud at a requecy o Hz. A obserer i a car traels away rom the soud source at a speed o 30.0 m/s. What is the requecy heard by the obserer? (assume the soud elocity 343 m/s) a) 513 Hz b) 713 Hz c) 913 Hz d) 1013 Hz e) 1113 Hz ƒ' ƒ + o s s 0, ( + ) ' o o 30m/s Hz 913Hz 343

7 Example Ah hor o trai emits soud with a requecy o 300 Hz whe the trai is at rest. The trai is moig at a speed o 100 km/h towards a obserer that is at rests. What is the requecy heard by the obserer? (assume the soud elocity 343 m/s) a) 75Hz b) 93 Hz ƒ' c) 300 Hz d) 313 Hz e) 37 Hz ƒ + o s O 0, 1000m 1h S 100km / h 7.8m / s km 3600s Hz 37Hz ' s

8 Coceptual quiz Three obserers,a,b, ad C are listeig to a moig source o soud. The diagram below shows the locatio o the waecrests o the moig source with respect to the three obserers.which o the ollowig is true? a. The waerots moe aster at A tha at B ad C. Waerots moe b. The waerots moe aster at C tha at A ad B. at soud speed 343 m/s c. The requecy o the soud is highest at A. d. The requecy o the soud is highest at B. e. The requecy o the soud is highest at C. soud λ λ is smallest at C is largest at C

Stadig waes o a strig L Two traelig siusoidal id waes o the same

a stadig wae: Because the strig is held at each ed, those poits

aishes. Ati-odes are the poits where the motio is maximal.

.. The geeral relatioship is: λ L λ ; λ Fig 14.18, p.

9 Stadig waes o a strig L Two traelig siusoidal id waes o the same requecy moig i opposite directios ca superimposed so as to make a stadig wae: Because the strig is held at each ed, those poits are odes o the oscillator motio, where the amplitude o motio aishes. Ati-odes are the poits where the motio is maximal. Motio with oe atiode has λ/ L, two atiodes has λl... The geeral relatioship is: λ L λ ; λ Fig 14.18, p. 443 udametal harmoics Slide 5 F 1,,3,,, L L μ 1 ud. C d Har. C 3 3 d Har. G 4 4 th Har. C 5 5 th Har. E

Example A stretched t strig ixed at each ed has a mass o 40.00 g ad a legth o 8.00 m.

(a) Determie the positios o the odes ad atiodes or the d harmoic.

10 Example A stretched t strig ixed at each ed has a mass o g ad a legth o 8.00 m. The tesio i the strig is 49.0 N. (a) Determie the positios o the odes ad atiodes or the d harmoic. (b) What is the ibratio requecy or this harmoic? Secod harmoic ( ) has odes at 0,4, ad 8 m ad ati-odes odes at ad 6 m. F L m/l Fig 14.18, p. 443 Slide 5 49N 98m/s 0.04kg / 8m as. 98m / s 1.4Hz L 8m

11 Stadig waes i a air colums: both eds ope I oe ed o the air colum is closed, a ode must exist at this ed sice the moemet o the air is restricted I the ed is ope, the elemets o the air hae complete reedom o moemet ad a atiode exists L λ 1,, 3,,, L

Let upward motio correspod to positie elocities.

12 Coceptual questio A strig is clamped at both eds ad plucked so it ibrates i a stadig mode betwee two extreme positios a ad b. Let upward motio correspod to positie elocities.whe the strig is i positio c, the istataeous elocity o poits alog the strig: a. is zero eerywhere. b. is positie eerywhere. c. is egatie eerywhere. d. depeds d o locatio. d d d

13 Stadig waes i a air colums: oe ed closed I oe ed o the air colum is closed, a ode must exist at this ed sice the moemet o the air is restricted I the ed is ope, the elemets o the air hae complete reedom o moemet ad a atiode exists 4L λ 13,, 5,,, 4L

14 Beats Beats are alteratios ti i loudess, due to itererece Waes hae slightly dieret requecies ad the time betwee costructie ad destructie itererece alterates beat 1

Sound II. Sound intensity level. Question. Energy and Intensity of sound waves

Sound II. Sound intensity level. Question. Energy and Intensity of sound waves Soud. Eergy ad tesity terferece of soud waes Stadig waes Complex soud waes Eergy ad tesity of soud waes power tesity eergy P time power P area A area A (uits W/m ) Soud itesity leel β 0log o o 0 - W/m