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PhysicsTutor
Doppler effect for EM waves
Giambattista 22.59
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Problem:
• A police car’s radar gun emits microwaves with frequency f1=36 GHz. The beam reflects from a car that speeds away from the cruiser with 43 m/s. The receiver in the police car detects the reflected waves at f2.
• Which frequency is higher, f1 or f2?
• Calculate the difference f2 – f1.
2
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Relevant ideas:
3
![Page 4: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/4.jpg)
Relevant ideas:
• The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer.
4
![Page 5: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/5.jpg)
Relevant ideas:
5
• The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer.
• In radar (emitting waves, observing frequency difference to waves reflected off a moving object) the Doppler effect appears twice.
![Page 6: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/6.jpg)
Relevant ideas:
• The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer.
• In radar (emitting waves, observing frequency difference to waves reflected off a moving object) the Doppler effect appears twice.
• EM waves travel in vacuum. No medium is involved. We treat air like vacuum here.
6
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Equations associated with ideas:
7
![Page 8: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/8.jpg)
Strategy
![Page 9: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/9.jpg)
Strategy
• Calculate the frequency of the radar waves as received by the speeding car.
![Page 10: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/10.jpg)
Strategy
• Calculate the frequency of the radar waves as received by the speeding car.
• The reflected waves have this shifted frequency, and are emitted from a moving source.
![Page 11: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/11.jpg)
Strategy
• Calculate the frequency of the radar waves as received by the speeding car.
• The reflected waves have this shifted frequency, and are emitted from a moving source.
• The receiver in the police car picks up the waves at a shifted frequency, since the source is moving away.
![Page 12: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/12.jpg)
Solution
![Page 13: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/13.jpg)
Solution
• _______________________
![Page 14: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/14.jpg)
Solution
• _______________________
• _______________________
![Page 15: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/15.jpg)
Solution
• _______________________
• _______________________
• _______________________
![Page 16: PhysicsTutor - York University•The Doppler effect for EM waves is derived in special relativity. It only involves the relative velocity between source and observer. •In radar (emitting](https://reader033.vdocuments.mx/reader033/viewer/2022041805/5e53dd8b9490e856c9434259/html5/thumbnails/16.jpg)
Solution
• _______________________
• _______________________
• _______________________
• _______________________