Physic 231 Lecture 35

Transcription

1 Physic 31 Lecture 35 Main points o last lecture: Waves transverse longitudinal traveling waves v wave λ Wave speed or a string v F µ Superposition and intererence o waves; wave orms interere. Relection o waves. Main points o today s lecture: Wave Sound speed waves: or a string Sound intensity: F v µ log Here F is the string tension 0 and µ is the mass/length. Superposition P/, 0 1x and intererence -1 W/m o Spherical waves; wave waves orms interere. Opp. P sign destructive. Same 4πr sign constructive Dopper Relection shit: o waves. rigid end inverted v + wave v o ree end non-inverted ƒ' ƒ wave v vs

2 Final Exam common inal exam time is scheduled or all sections o Physics 31 Time: 8:00-:00 PM, Tues., Dec. 1 Each section has a dierent exam location. Location or Section 1: Wells Hall 6 n alternate exam time has been scheduled or students who have conlicts with the regular time. Three students have conirmed conlicts with me and will take the exam then. You must have permission rom me to take the exam at the alternate time. lternate time: 7:45-9:45 M, Monday, Dec. 11 Location: PS 1415 (this room)

3 onceptual question wave pulse is moving, as illustrated, with uniorm speed v along a rope.which o the graphs 1 4 below correctly shows the relation between the displacement s o point P and time t?

4 Sound amplitude and intensityv v The amplitude o the sound wave is proportional to the maximum velocity o the air as it moves rom the high pressure to the low pressure domains. The energy and the power o the sound wave is proportional to the square o amplitude: 1 E ρv mplitude vmax p xmax More useul than the energy o a sound wave is the intensity,, which is the power P that the sound wave transmits per unit area. P E The ear responds logarithmically to the intensity o sound waves striking the eardrum. threshold 0-1 W/m, pain 1 W/m This logarithmic behavior motivates the decibel measure o sound wave intensity. log (/ 0 ) ( T ) Fig 14., p. 46 Slide 4

5 Historical note: Decibel is named ater lexander Graham ell

6 Example The intensity level o sound is 5.0 d greater than that o sound and 3.0 d less than that o sound. a) Determine the ratio ( / ) o the intensity o sound to the intensity o sound. b) Determine the ratio o the amplitudes p /p o the modulation in pressure caused by the sound wave. ( ) ( ) log 8 3) ( 5 log 3 log 5 log log log log ) 1/ p p a

7 Propagation o spherical and plane waves. one vibrates as piston in a tube o cross-sectional area, the sound waves travel down the tube in a straight line, like a wave on a string. The sound wave power P crossing point and point per unit time are the same. Since the area o the tube is constant, the intensity P/ is the same at both points. one suspends non-directional sound source with power P in air, the sound will radiate in all directions. ll points on a sphere o radius r will see the same sound intensity: P 4πr r Fig 14.4, p. Slide 8

8 Example When a helicopter is hovering 10 m directly overhead, an observer on the ground measures a sound intensity. ssume that sound is radiated uniormly as a spherical wave rom the helicopter and that ground relections are negligible. How ar must the helicopter ly in a straight line parallel to the ground beore the observer measures a sound intensity o 1/5? m h d h d h r d h r r P r P / π π

9 wave is sent along a long spring by moving the let end rapidly to the right and keeping it there.the igure shows the wave pulse at QR part RS o the long spring is as yet undisturbed. Which o the graphs 1 5 correctly shows the relation between displacement s and position x? (Displacements to the right are positive.) onceptual problem

10 Doppler eect or moving observer Fig 14.8, p. 435 Slide 1 Fig 14.9, p. 436 Slide 13 n observer is moving toward a stationary source Due to his movement, the observer detects an additional number o wave ronts The requency heard is increased n observer is moving away rom a stationary source The observer detects ewer wave ronts per second The requency appears lower

11 Doppler Eect, Source in Motion general ormula ƒ' ƒ v v + v v o s oth the source and the observer could be moving s the source moves toward the observer (), the wavelength appears shorter and the requency increases s the source moves away rom the observer (), the wavelength appears longer and the requency appears to be lower Use positive values o v o and v s when the motion is toward Frequency appears higher Use negative values o v o and v s when the motion is away Frequency appears lower

12 Example train at rest emits a sound at a requency o Hz. n observer in a car travels away rom the sound source at a speed o 30.0 m/s. What is the requency heard by the observer? (assume v s 343 m/s) a) 513 Hz b) 713 Hz v 0, v 30m / s c) 913 Hz d) 13 Hz e) 1113 Hz s ' ( v + v ) v o o Hz 913Hz 343

13 onceptual quiz Three observers,,, and are listening to a moving source o sound. The diagram below shows the location o the wavecrests o the moving source with respect to the three observers.which o the ollowing is true? a. The waveronts move aster at than at and. b. The waveronts move aster at than at and. c. The requency o the sound is highest at. d. The requency o the sound is highest at. e. The requency o the sound is highest at.

14 Example Two trucks travel at the same speed. They are ar apart on adjacent lanes and approach each other essentially head-on. One driver hears the horn o the other truck at a requency that is 1. times the requency he would hear i the trucks were stationary. The speed o sound is 343 m/s. t what speed is each truck moving? givens : ' ans. ( v + vo ) ( v v ) ' ' s 1. 1., ( v + v ) ( v v ) ( v + v ) ( v v ) v 31m / s v s v o v