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Doppler effect

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Brief history on Doppler effect, concept of Doppler, and it application to real world

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Doppler effect

  1. 1. Tuesday session # 2 Tuesday Session # 2 Doppler Effect Tuesday Session # 2
  2. 2. Doppler effect  What do you observed when you throw a pebble into a body of water? (apart from the pebble sinking) 2
  3. 3. Doppler effect  Doppler effect explained why we perceives a change in frequency when the wave source approaches or retreat from us… 3
  4. 4. Doppler effect What is doppler effect?  Doppler effect is the change in frequency of a wave for an observer moving relative to its source.  the observer observes an upward shift in frequency when the wave source is approaching,  And a downward shift in frequency when the wave source is retreating 4
  5. 5. Doppler effect  Doppler effect applies to all waves including;  Sound waves,  Light waves  Water waves 5
  6. 6. Doppler effect  Doppler effect originated in 1842 by an Austrian physicist “Christian Doppler”.  Christian Doppler proposed doppler effect in his article "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels”.  Translated as “On the coloured light of the binary stars and some other stars of the heavens”. 6
  7. 7. Doppler effect  Doppler’s hypothesis was tested for sound wave Buys Ballot in 1845.  Who confirmed that the frequency of sound’s pitch emitted was higher than frequency when the sound source approached him,  and lower than the emitted frequency when the sound source receded from him.  Hippolyte Fizeau found similar result in electromagnectic waves (1848)  John Scott Russell (1848) 7
  8. 8. Concept of Doppler effect  To understand the concept of doppler effect we must first understand the following;  Wavelength  Frequency  Velocity 8
  9. 9. Concept of Doppler effect Wavelength  The distance between two successive crest of a wave, especially points in a sound wave or electromagnetic wave. 𝝀 = 𝝊 𝒇  𝜆 – wavelength  𝜐 – speed  𝑓 – frequency 9
  10. 10. Concept of Doppler effect Frequency  The number of occurrence of repeating event per unit time.  In terms of waves, it’s the number of waves passing a given point per unit time.  Unit of frequency is hertz 𝒇 = 𝝂 𝝀 10
  11. 11. Concept of Doppler effect Velocity  The speed of something (waves) in a given direction. 𝐯 = 𝐝 𝐭  v – velocity  d - displacement  t - time 11
  12. 12. Concept of Doppler effect Water waves  Imagine you are swimming with your friend Paul, and he is constantly bobbing his head up and down creating a stream of wave reaching you at the end of the pool.  You observed that at every 2 second interval 3 wave reaches you.  As such the frequency of the wave observed is; 𝒇 = 𝟑 𝟐. 𝟎𝒔 = 𝟏. 𝟓𝐇𝐳 12
  13. 13. Concept of Doppler effect  Now, you decide to call Paul to enlighten him on your brilliant observation.  Paul decide to continue his repeated bobbing as he approaches you. As he did so you notice something else.  Instead of 3,you observes 4 waves reaching you every 2 second.  The frequency observes is thus; 𝒇 = 𝟒 𝟐. 𝟎𝒔 = 𝟐𝐇𝐳 13
  14. 14. Concept of Doppler effect  You got so excited about your find, that you were speechless when Paul arrives.  So Paul decided to return to his previous position in pool, still continuously bobbing.  Paul lost focus of his intention and went pass his original position.  You detected his lost of focus and decide to call out to him,  But before you could you notice another phenomena. 14
  15. 15. Concept of Doppler effect  This time, instead of 3 waves per 2 second, you observed that only 1 wave reaches you every 2 second.  Which implies that the frequency of wave approaching has decline. 𝒇 = 𝟐 𝟐. 𝟎𝒔 = 𝟏𝐇𝐳 15
  16. 16. Concept of Doppler effect Sound waves  A siren on a police car (source) emitting a uniform series of sound waves, moving away from the source in all direction.  Jason a distance away observing (observer)  Air stationary (assumption) 16
  17. 17. Concept of Doppler effect  Lets take the wavelength to be 𝝀, the frequency to be 𝒇 and the speed of the sound to be 𝝂.  𝝂 𝒐 and 𝝂 𝒔 represent the speed of the observer and the source respectively. 17
  18. 18. Concept of doppler effect  If both the observer and the source were stationary, he would observe a frequency equal to that of the source. 𝝂 𝟎 = 𝟎 and 𝝂 𝒔 = 𝟎 18
  19. 19. Concept of Doppler effect  If the observer decide to walk towards the source, the speed of the waves in relation to the observer; 𝝂′ = 𝝂 + 𝝂 𝒐  The wavelength 𝝀 however remains the same.  Therefore the frequency 𝒇′ observes by the observer is; 19
  20. 20. Concept of Doppler effect 𝒇 = 𝝂′ 𝝀 𝒇 = 𝒗 + 𝒗 𝒐 𝝀  Since 𝝀 = 𝝂 𝒇 frequency of observer can be express as; 𝒇′ = 𝝂+𝝂 𝒐 𝝂 𝒇  Frequency observed by the observer increases. 20
  21. 21. Concept of Doppler effect  If the observer decided to walk away from the source, the speed of the waves relative to the observer is; 𝑣′ = 𝜈 − 𝜈 𝑜 𝑓′ = 𝜈 − 𝜈 𝑜 𝜈 𝑓  The frequency heard by the observer in this scenario is decrease. 21
  22. 22. Concept of Doppler effect  Now suppose the vehicle (source) is moving toward to the observer who is at rest.  Since the source is moving towards the right, each successive wave is emitted from a position closer to the observer than the previous wave.  As a result, the wave fronts heard by the observer are closer together than they would be if the source were not moving. 22
  23. 23. Concept of Doppler effect  The wavelength 𝝀′ therefore measured by the observer is shorter than the wavelength 𝝀 of the source.  For every consecutive wave which last for a time interval T, the source moves a distance 𝝂 𝒔 𝑻 = 𝝂 𝒔 𝒇 .  The wavelength is shorten by this amount 23
  24. 24. Concept of Doppler effect  The wavelength 𝜆′ observe is thus 𝝀′ = 𝝀 − 𝜟𝝀 = 𝝀 − 𝝂 𝒔 𝒇  Since 𝜆 = 𝜈 𝑓 , the observe frequency 𝒇′ is 𝒇′ = 𝝂 𝝀′ = 𝝂 𝝀 − (𝝂 𝒔 𝒇) = 𝝂 𝝂 𝒇 𝝂 𝒔 𝒇 𝒇′ = 𝝂 𝝂 − 𝝂 𝒔 𝒇  The observes frequency increases as the sources is moving toward the observer. 24
  25. 25. Concept of Doppler effect  Conversely, if the source is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave,  So the arrival time between successive waves is increased, reducing the frequency. 𝒇′ = 𝝂 𝝂+𝝂 𝒔 𝒇 25
  26. 26. Concept of Doppler effect  The general Doppler effect 𝒇′ = 𝝂 + 𝝂 𝒔 𝝂 − 𝝂 𝒐 𝒇  This equation applies to all four conditions mention previously.  The sign of 𝜈𝑠and 𝜈 𝑜depend on the direction of the velocity.  A positive value is used for motion of the observer or the source toward the other, and a negative value is used for motion of one away from the other. 26
  27. 27. Application of Doppler effect  In the 1600 years or so since Doppler first described the wave phenomenon that would cement his place in history, several practical applications of the Doppler effect have emerged to serve society.  In all of these applications, the same basic thing is happening. 27
  28. 28. Application of Doppler Effect  One application of Doppler effect found in nature, occurs in bats hunting for their prey.  Bats navigates it’s flight by emitting whistles and listening for the echoes.  When chasing prey, its brain detects a change in pitch between the emitted whistle, and the echo it receives.  This tells the bat the speed of its target, and the bat adjusts its own speed accordingly. 28
  29. 29. Application of Doppler Effect Radar  The Doppler effect is used in some types of radar, to measure the speed of detected objects.  For example a police officer uses radar guns to check for speeding vehicles.  The radar gun emits waves at a particular frequency, which when strikes the vehicles bounce back toward the gun.  The radar gun then measure the frequency of the returning waves, then eventually determine the speed. 29
  30. 30. Application of Doppler effect  Doppler radar (radar in general) is a form of technology used not only by law-enforcement officers, but also by meteorologists.  Meteorologists utilize Doppler effect to determine the direction and velocity of raindrops, wind direction and other weather events.  This principle is very crucial as it allows meteorologist to predict weather pattern including coming storm etc. 30
  31. 31. Application of Doppler effect Medical diagnosis  Physicians and medical technicians apply Doppler effect to measure the rate and direction of blood flow in a patient's body, along with ultra-sound.  Ultrasound beam are pointed towards an artery, and the reflected waves exhibit a shift in frequency, because the blood cells are acting as moving sources of sound waves.  An echocardiogram uses sound waves transmitted by ultrasound to produce images of the heart (transducer transmit and receive waves, which are reflected when they reach the edge of two structures with different densities). 31
  32. 32. Application of Doppler effect Flow Measurement  Instruments such as the laser Doppler velocimeter (LDV), and Acoustic Doppler Velocimeter (ADV) have been developed to measure velocities in a fluid flow.  A light beam or an ultrasonic acoustic burst is release by the LDV and ADV respectively, subsequently measuring the shift in wavelengths of reflections from particles moving with the flow.  This technique allows non-intrusive flow measurements, at high precision and high frequency. 32
  33. 33. Application of Doppler effect Satellite Communication  Satellite employs Doppler effect in its tracking technique for determining distance between satellite and receiver at the time of closest approach as well as the time itself.  Approaching satellite increases the frequency relative to the actual transmission frequency.  As it retreats, the frequency lowered. At the time of closest approach, the transmitted and received frequencies are usually the same. 33
  34. 34. Application of Doppler effect  Doppler effect has found its use in several other area which includes;  Astronomy  Vibration measurement  To Sense Gesture (computer base)  Audio  Velocity profile measurement etc. 34
  35. 35. References  Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.  Bryant-Mole, Karen. Sound and Light. Crystal Lake, IL: Rigby Interactive Library, 1997.  Challoner, Jack. Sound and Light. New York: Kingfisher, 2001.  Dispenzio, Michael A. Awesome Experiments in Light and Sound. Illustrated by Catherine Leary. New York: Sterling Publishing Company, 1999.  "The Doppler Effect." The Physics Classroom (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l3 .html> (April 29, 2001).  Maton, Anthea. Exploring Physical Science. Upper Saddle River, N.J.: Prentice Hall, 1997.  Russell, David A. "The Doppler Effect and Sonic Booms" Kettering University (Web site). <http://www.kettering.edu/~drussell/Demos/doppler/doppler.htm > (April 29, 2001).  Snedden, Robert. Light and Sound. Des Plaines, IL: Heinemann Library, 1999.  "Sound Wave—Doppler Effect" (Web site). <http://csgrad.cs.vt.edu/~chin/doppler.html> (April 29, 2001).  "Wave Motion—Doppler Effect" (Web site). <http://members.aol.com/cepeirce/b21.html> (April 29, 2001).  D’Ambrose, C. “Frequency Range of Human Hearing”.The Physics Factbook 2003. Downloaded 10/1/2011.  2. Ditchburn, R.W. Light. Dover publications, p. 331-333.1961, 1991.  3. Paradiso, J., Abler, C., Hsiao, K. and Reynolds, M. The magic carpet: physical sensing for immersive environments.In Proc. ACM CHI 1997. 35
  36. 36. .  Alec Eden The search for Christian Doppler,Springer-Verlag, Wien 1992. Contains a facsimile edition with an English translation.  Buys Ballot (1845). “Akustische Versuche auf der Niederländischen Eisenbahn, nebst gelegentlichen Bemerkungenzur Theorie des Hrn. Prof. Doppler (in German)".Annalen der Physik und Chemie 11: 321– 351.doi:10.1002/andp.18451421102.  [3] Fizeau: “Acoustique et optique”. Lecture, Société Philomathiquede Paris, 29 December 1848. According to Becker(pg. 109), this was never published, but recounted by M. Moigno(1850): “Répertoire d'optique moderne”(in French), vol 3. pp 1165-1203 and later in full by Fizeau, “Des effets du mouvement sur le ton des vibrations sonores et sur la longeur d'onde des rayons de lumière"; [Paris, 1870]. Annales de Chimie et de Physique,19, 211-221.  Scott Russell, John (1848). “On certain effects produced on sound by the rapid motion of the observer”. Report of the Eighteenth Meeting of the British Association for the Advancement of Science (John Murray, London in 1849) 18  (7): 37–38. Retrieved 2008-07-08.  [5] Rosen, Joe; Gothard, Lisa Quinn (2009). Encyclopedia of Physical Science. Infobase Publishing. p. 155. ISBN 0-8160-7011-3., Extract of page 155  Evans, D. H.; McDicken, W. N. (2000). Doppler Ultrasound  (Second ed.). New York: John Wiley and Sons.ISBN 0-471-97001-8.  [8] Qingchong, Liu (1999), “Doppler measurement and compensation  in mobile satellite communications systems”, Military Communications Conference Proceedings / MILCOM1: 316–320, doi:10.1109/milcom.1999.822695  [9] The Inverse Doppler effect: Researchers add to the bylaws of physics, physorg.com, May 23, 2005, retrieved 2008-03-08 [10] Scientists reverse Doppler Effect, physorg.com, March 7, 2011, retrieved 2011-03-18 36
  37. 37. . Wang, S., Doppler Effect in Sound, Phys. Teach. 9, 12(2006). In Chinese.  [2] Jackson, J. D., Classical Electrodynamics, 3rd edition,(John Wiley & Sons, Inc., Hoboken, NJ, 1999) Chap. 11,pp. 518 – 519.  [3] Hay, H. J., Schiffer, J. P., Granshw, T. E. and Egelstaff, P. A., Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in Fe,Phys. Rev. Lett. 4, 165 (1960).  Tarzia, S.P, Dick, R.P. Dinda, P.A and Memik, G. Sonar-based measurement of user presence and attention.In Proc. ACM UbiComp 2009  Abrahsm, M., Zur Theorie der Strahlung und des Strahlungsdruckes, Ann. Phys. Leipzig, 14, 236-287, 1904.  Borkar, R. S., and R. F. H. Yang, Scattering  of electromagnetic waves from rough oscillating surfaces using spectral Fourier method, IEEE Trans. ,  Antennas Propag.,AP-21.., 734-736, 1973. Borkar, R. S., and R. F. H. Yang,  Reflection of electromagnetic waves from oscillating surfaces, IEEE Trans. Antennas Propag., AP-23, 122-127, 1975.  Brandstatter, J. J., Rays and Radiation in Plasma Media, 690 •p., McGraw-Hill, New York, 1963. 37

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