2/11/2006 Doppler ( F.Robilliard) 1

Transcription

1 2//2006 Doppler ( F.obilliard)

2 Deinition o Terms: The requency o waes can be eected by the motion o either the source,, or the receier,, o the waes. This phenomenon is called the Doppler Eect. We will consider this eect or sound waes. M ource,, emits waes into the medium, M, through which they trael to a receier,. requency transmitted by source,. requency receied by receier,. requency o ibration in the medium elocity o the source, relatie to the medium. elocity o the receier, relatie to the medium. elocity o the wae, relatie to the medium. λ waelength o waes in the medium. 2//2006 Doppler ( F.obilliard) 2

3 Waeronts: ound waes are transmitted rom their source, in three dimensions. Waeronts are a graphical representation o the progress o the wae through space. Deinition: A waeront is a surace on which all points o the wae motion hae the same phase. Example: A stone dropped into water sends out ripples. The crest o a ripple is a waeront. The trough o a ripple is another waeront. A point source produces spherical waeronts. A ray is a line drawn to represent the direction o the wae elocity - the direction o trael o the wae. ays are perpendicular to waeronts. We need this notion o waeronts to analyse the Doppler Eect. 2//2006 Doppler ( F.obilliard) 3

4 Moing eceier: Firstly we consider the case o a receier moing, with a elocity,, toward a stationary source. The source,, emits waeronts per second. I the receier,, were stationary, waeronts would pass oer it, per second Because is moing at a elocity o, it will cross an additional ( / λ) waeronts per second, where λ is the waelength the distance between successie waeronts, in the medium. The receier requency,, is the number o waeronts that cross it, per second 2//2006 Doppler ( F.obilliard) 4

5 But And Thus Hence eceier Frequency: since the source is stationary in the medium moing toward. I instead o moing toward the source, the receier moed away, then it would detect correspondingly less waeronts per second. Thus: moing away rom. will measure a higher/lower requency, i it moes toward/away rom. 2//2006 Doppler ( F.obilliard) 5

6 Animation: A stationary receier,, receies waeront per second. Hz. λ s I moes toward the source,, a distance o waelength each second, extra waeront will pass oer, each second. Then 2 Hz. 2//2006 Doppler ( F.obilliard) 6

7 Moing ource: econdly we consider the case o a source, moing with a elocity,, toward a stationary receier. Thereore, the waelength, λ, between and is: Once emitted by a point source, waeronts expand spherically rom the point o emission., 2, 3, 4 represent the positions o the source when the our waeronts shown were emitted Waeronts on the receier side o the source, are bunched up. The waelength, λ, is shorter, than i the source had been stationary. waeronts are emitted per second by the source. These waeronts are distributed oer a distance o ( ). range o waeronts number o waeronts ( ) 2//2006 Doppler ( F.obilliard) 7

8 ( ) eceier Frequency: But, the receier requency,, is the number o waeronts passing the receier per second. Thus: speed o wae in medium waelength ( - ) moing toward I is moing away rom, a corresponding increase in the waelength between and produces: moing away rom The receier measures a (higher)/(lower) requency i the source is moing (toward)/(away rom) the receier. 2//2006 Doppler ( F.obilliard) 8

9 Animation: Waeronts crowd up in ront o the moing source,. More waeronts hit receier,, per second, giing a higher receier requency. 2//2006 Doppler ( F.obilliard) 9

10 Both ource & eceier Moing: ay both and are moing toward each other relatie to the medium. M hit rom source,, to medium, M: ( Moing, stationary M)... ( ) Let requency o ibrations in the medium. There are two components to the oerall Doppler shit here. A shit rom to medium, and a shit rom medium to. hit rom medium, M, to receier, : ( tationary M, moing )... 2//2006 Doppler ( F.obilliard) 0 ( ) ( 2) : ( 2) & moing toward each other

11 2//2006 Doppler ( F.obilliard) ummary: ± General Acoustic Case For: I reersed : replaced by (- ) I reersed : replaced by (- ) I stationary : 0 I stationary : 0

12 Doppler or Light: The Doppler Eect or electromagnetic waes, such as light, is a little dierent. There is no physical medium light traels though a acuum. Only the relatie elocity,, between the source,, and the receier,, is meaningul. Also the speed o light, c, in the acuum, is always the same, or all obserers, independent o their motion. For approaching and, the result is: Applications o Doppler: () The elocity o blood in the body can be measured by ultrasound Doppler. (2) Doppler shits in signals rom a satellite gies the in-line elocity o the satellite. (3) Velocities o stars and galaxies is measured by Doppler red shit expanding unierse. (4) peed o motor ehicles can be measured by Doppler radar. 2//2006 Doppler ( F.obilliard) 2 c c Electromagnetic case

13 C Example: A train approaching a tunnel receies an echo o its whistle rom the cli aboe the tunnel. I a 000 Hz whistle echoes as 050 Hz, ind the speed o the train. Let: whistle requency 000 Hz echo requency 050 Hz C requency receied by cli t speed o train speed o sound 340 m/s The cli receies a Doppler shited requency, C, due to the motion o the train, as a moing source, where: t... The cli echoes back the requency C. The train receies a Doppler shited requency,, due to the motion o the train, as a moing receier, where: ( ) C t... ( 2) 2//2006 Doppler ( F.obilliard) 3

14 2//2006 Doppler ( F.obilliard) 4 Example: ( ) ( ) ( ) 8.29 m/s where 2 t t t t t

15 2//2006 Doppler ( F.obilliard) 5