INTRO VIDEOS. LESSON 9.5: The Doppler Effect

Transcription

1 DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS INTRO VIDEOS Big Bang Theory of the Doppler Effet Doppler Effet LESSON 9.5: The Doppler Effet 1. Essential Idea: The Doppler Effet desribes the phenomenon of wavelength/frequeny shift when relative motion ours. 2. Nature Of Siene: a. Tehnology: Although originally based on physial observations of the pith of fast moving soures oound, the Doppler Effet has an important role in many different areas suh as

2 evidene for the expansion of the universe and generating images used in weather reports and in mediine. 3. International-Mindedness: Radar usage is affeted by the Doppler Effet and must be onsidered for appliations using this tehnology. 4. Theory Of Knowledge: How important is sense pereption in explaining sientifi ideas suh as the Doppler effet? 5. Understandings: The Doppler Effet for sound waves and light waves. 6. Appliations And Skills: a. Skething and interpreting the Doppler Effet when there is relative motion between soure and observer. b. Desribing situations where the Doppler Effet an be utilized.. Solving problems involving the hange in frequeny or wavelength observed due to the Doppler Effet to determine the veloity of the soure/observer. 7. Guidane: a. For eletromagneti waves, the approximate equation should be used for all alulations

3 b. Situations to be disussed should inlude the use of Doppler effet in radars and in medial physis, and its signifiane for the red-shift in the light spetra of reeding galaxies 8. Data Booklet Referene: a. Moving soure: f = f ( v v±u s ) b. Moving observer: f = f ( v±u s v ). f f = λ λ v 9. Utilization: Astronomy relies on the analysis of the Doppler effet when dealing with fast moving objets (see Physis option D) 10. Aims: a. Aim 2: the Doppler effet needs to be onsidered in various appliations of tehnology that utilize wave theory b. Aim 6: spetral data and images of reeding galaxies are available from professional astronomial observatories for analysis. Aim 7: omputer simulations of the Doppler effet allow students to visualize omplex and mostly unobservable situations

4 3. Definition: The Doppler Effet is the hange in the frequeny of a wave reeived by an observer ompared with the frequeny with whih it was emitted. The effet takes plae whenever there is motion between the emitter and reeiver. a) Consider first a stationary soure:

5 a) Now onsider a moving soure: b) The time between wavefronts is the period, T ) If the soure is travelling at a speed v s, in the time between emitting two suessive wavefronts (T), the soure will have moved a distane of d s = v s T d) To the observer, the reeived wavelength will be λo = λs-d s

6 4. Derivation e) for soure moving toward observer: λ o = λ s d s = λ v s T T = 1 f f = λ T = λ λ o = λ s v s λ s λ o = λ s (1 v s ) i) Sine λ o is the wavelength pereived by the observer and sine f =, then the λ frequeny pereived by the observer is λ o λ s (1 v s) Sine =, we an fator this out, λ s 1 (1 v s )

7 (1 v s) a) for soure moving away from the observer: ii) The differene will be that the observed wavelength will be greater than the wavelength emitted by the soure by an amount equal to the distane travelled by the soure in the time between emissions, whih is the period, T λ o = λ s + d s = λ + v s T i) Using the same derivation as above, the result is (1 + v s ) a) For observer moving toward soure: i) While you would think the same formulas would work, this situation is different. ii) In this situation, the wavelength pereived by the observer is the same as that emitted by the soure (λ o = λ s ), only the veloity of the waves is hanged with respet to the observer

8 iii) In other words, sine the soure is stationary, the waves it emits are all still the same distane apart. But sine the observer is moving toward the soure, he pereives the waves as oming at him more quikly by an amount equal to v =+v o iv) This will, in turn, affet the frequeny: v λ s = + v o λ s Sine = λ s and λ s =, + v o + v o (1 + v o ) (1 + v o ) a) For observer moving away from soure: i) Using the same line of thinking, in this situation the pereived wavelength is still the same as that emitted by the soure, but beause the observer is moving away from

9 the soure, the waves hit the observer at a lower veloity, v =-v o ii) Using the same derivation, the result is (1 v o ) 5. Summary of the four ases: a) Soure moving toward observer: (1 v s) a) Soure moving away from observer: (1 + v s) b) Observer moving toward soure: (1 + v o ) ) Observer moving away from soure: (1 v o )

10 6. What formulas are you provided with in your Data Guide? Tsokos Moving Soure: (1 v s) (1 + v s) Moving Observer: (1 + v o ) (1 v o ) Data Guide Moving Soure: f v = f (v ± u s ) Moving Observer: f = f v ± u o (v) 7. Note that in the ase of a moving soure, the pereived (and atual) wavelength hanges, but with a moving observer, the wavelength is the same. That is why we define the Doppler Effet in terms of observed frequeny.

11 SUMMARY VIDEO The Doppler Effet LESSON 9.5: HOMEWORK #36-49