Doppler Effect

March 29, 2018 | Author: krawczyb | Category: Medical Ultrasound, Redshift, Doppler Effect, Ultrasound, Medical Imaging


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DOPPLER EFFECTRevise basic concepts • The wavelength, λ, is the distance between any two successive identical points on a wave • The frequency, f, is the number of crests – or complete cycles – that pass a given point per second. The unit of frequency is hertz (Hz) • The period, T, equals 1/f and is the time elapsed between two successive crests passing by a fixed point. • The relation between frequency (f) and period (T): f=1/T or T=1/f • • • The amplitude, A, is the maximum height of a crest, or depth of a trough, relative to the rest position. The pitch of sound is determined by the frequency; the higher the frequency, the higher the pitch. The wave velocity, v, is the velocity at which wave crests (or any other part of the waveform) move. Velocity = frequency x wavelength v= f x λ Activity 1 Prior knowledge WAVES TRAVELING IN WATER Complete the following activity in groups and give feedback to the larger group. Scenario 1 A stationary bug is jiggling its legs and bobbing up and down in the middle of a quiet puddle (remaining in a fixed position).  Discuss this scenario in terms of: the pattern, frequency and distance between wave crests (the wavelength) of successive waves.  Complete the drawing below.  Explain what is encountered by the observer in positions A and B? A B Top view of water waves made by stationary bug jiggling in still water. Scenario 2 Suppose the jiggling bug now moves across the water with a speed less than that of the wave speed.  Discuss this scenario in terms of: pattern, frequency and distance between wave crests (the wavelength) of successive waves.  Complete the drawing below.  Explain what is encountered by the observer in positions A and B? A B A top view of water waves made by bug swimming to the right in still water Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 1 Explain the above phenomenon in terms of changing pitch (low or high sound).1 while the train is approaching 1. the frequency (number of waves per second) and amplitude (loud or soft) of sound waves encountered by the observer. watching the train approach and then pass by. Present your explanations in a table.Activity 2 Answer the questions in groups: DOPPLER EFFECT FOR SOUND WAVES 1. calculate the whistle frequency that Japie hears: 1. What is your understanding of: “an apparent change in frequency?” 4. the frequency is lower. 1.2 Doppler effect v ± vl fs 1. Note: The frequency is higher when the observer and source approach each other and lower when they move apart. When the source (S) is moving towards the listener (L) the frequency becomes higher than that of the source at rest. Give examples of encountering the Doppler Effect in everyday life.2 while the train is moving away from him. the lower signs apply if they are moving apart.2 What is the name of this phenomenon? 1.1 What change in the pitch of the sound does Japie notice as the train approaches him? 1. Example 11: On a windless day a train approaches a level crossing at 30 m∙s-1 with its whistle blowing continuously. 3.1 Increased pitch 1. This apparent change frequency is due to the motion of the source (or receiver) and is called the Doppler Effect. Thus the upper signs in numerator and denominator apply if source and/or object move toward each other.3. What does the observer hear while the truck moves towards him. passes him and moves away from him? 2. Japie stands at the crossing. The Doppler Effect can be explained in terms of a change in the frequency or pitch of sound when either the listener (L) or the source (S) is moving with respect to each other. Activity 3 fl = THE DOPPLER EQUATION v ± vl fs v v s fl = frequency heard by the listener fs = frequency emitted by the source v = speed of sound in air 340 m∙s-1 vs= velocity of the source vl = velocity of the listener.3.1 f l = v v s 340 + 0 456 = 340 − 30 1 Example with permission taken from: OBE for FET Physical Sciences Exam Study Guide Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 2 . and when the source travels away from the listener.3 If the frequency of the train whistle is 456 Hz and the speed of sound on that day is 340 m∙s-1. Solution: 1.3. usually with ultrasonic waves in the megahertz frequency range e.50 340 5051 .47 = 52.03 Hz = Example 2 A 5 000 Hz sound wave is emitted by a stationary source.47 Hz (ii) The moving object now “emits” (reflects) sound of frequency fL(emitted).5 = 5 104.54 Hz The above Doppler technique is used in a variety of medical applications.3. fL(detected).g to measure the rate of blood flow or the heart of a fetus.50 m∙s-1 (vL) to detect the sound wave of frequency. Check your progress: A Doppler flow meter uses ultrasound waves to measure blood-flow speed.50 m∙s-1 (i) fL(detected) is the frequency “detected” by the moving object f det ectedl = = v ± vl fs v v s 340 + 3.5 5000 = 340 = 5 051. f emitted = = = v ± vl fs v vs 340 + 0 5051 .5 MHz.13 Hz v ± vl fs 1.50 5000 340 − 0 343 . Suppose the device emits sound at 3. The source is moving towards the detector. (ii) The reflection of the wave from the moving object is equal to the object reemitting the wave. and the speed of sound in human tissue is taken to be 1540 m∙s-1 .50 m∙s-1 toward the source. Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 3 .01 Hz Thus the frequency shifts by 5 104.2 f l = v v s 340 + 0 456 = 340 + 30 340 456 = 370 = 419. What is the frequency of the wave reflected by the moving object as detected by a detector at rest near the source? Solution: There are two Doppler shifts.47 340 − 3.01 – 5 051. This sound wave reflects from an object moving 3.0 m∙s-1 directly away from the sound source? APPLICATIONS OF THE DOPPLER EFFECT • Weather forecasting using radar.47 336 . This is similar to the frequency detected by the moving object (source) and stationary observer.340 456 310 = 500. (i) The moving object acts like an observer (listener) moving towards the source with speed vobs= 3. What is the expected beat frequency if blood is flowing in large leg arteries at 2. The time delay between emission of radar pulses and their reception after being reflected off raindrops gives the position of precipitation. acting as a moving source with speed vS = 3. its light will be shifted to longer (red) wavelengths. Statement 1: “the amount of "red shift" was proportional to distance” Statement 2: “if an astronomical object is moving away from the Earth." Doppler shift is what makes a car sound lowerpitched as it moves away from you. DOPPLER EFFECT FOR LIGHT Activity 4 In groups read the following excerpt The "Red Shift” Early in this century. In 1929 astronomer Edwin Hubble compared the galaxies' spectra with their distances. and the farther the galaxy. Hubble and others realized that the most obvious explanation for the "red shift" was that the galaxies were receding from Earth and each other. Tumors and other abnormal growth can be distinguished.arachnoid. Receding Advancing http://www. Ultra-sonic frequency (higher than 20 kHz) sound waves are used:  to locate underwater objects.” Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 4 .if an astronomical object is moving away from the Earth.com/sky/redshift. and showed that the amount of "red shift" was proportional to distance. astronomers noticed that distant galaxies had peculiar light spectra. its light will be shifted to longer (red) wavelengths. How the red shift in light waves can be linked to the Doppler Effect in sound waves? 2. the action of heart valves and the development of a fetus can be examined. the faster the recession.  for medical imaging.Measuring the Doppler shift in frequency tells how fast the storm is moving and in which direction. the galaxies' light spectra were shifted toward the red end of the spectrum. the depth of the sea. It turns out that a special version of this everyday effect applies to light as well -. Explain in your groups: 1. the location of reefs or sunken ships. Red-shift examples This conclusion is based on a cosmological effect that is similar to the everyday "Doppler shift.html These examples are greatly exaggerated. • Sonar (sound navigation range). Explain your understanding of the statements below taken from the text above. calculated using different methods. Specifically. What is meant by “the bug is encountering a wave barrier”? 3. SHOCK WAVES AND THE SONIC BOOM Activity 5 Wave barriers. while the frequency of yellow light is about 5 x 1014 Hz. Interpret the above statement and complete a drawing showing the wave pattern made by the bug swimming faster than wave speed. What is meant by the following?  An aircraft cracking the sound barrier?  A sonic boom?  A supersonic aircraft?  An object moving at Mach 3? 2 Example with permission taken from: OBE for FET Physical Sciences Exam Study Guide Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 5 .1 the wavelength of the sound wave 1. Answer the questions in groups: 1. it outruns the waves it produces. is called a bow wave. calculate: 1.2 the wavelength of yellow light. Assuming that sound travels at 340 m∙s-1 in air and light at 3 x 108 m∙s-1. Sound travels at ±343 m/s in air.Check your progress 22: 1. it finds the water ahead relatively smooth and undisturbed. Are the water waves produced by the swimming bug still ahead of the bug? 2. dragging behind the bug.) A B A top view of a bow wave made by bug swimming to the right faster than wave speed 5. When the bug swims faster than wave speed.” 4. A B A top view of water waves made by bug swimming to the right at wave speed Scenario 4: “Once the bug is over the wave barrier. shock waves and sonic boom Scenario 3 Suppose the jiggling bug now moves across the water with the same speed as wave speed. (The V-shaped pattern made by overlapping waves. A typical sound wave associated with human speech has a frequency of 500 Hz. bow waves. Complete a drawing below showing the wave pattern made by the bug swimming at wave speed. 6. A mother hawk screeches as she dives at you. a) a person standing beside the road in front of the car? b) a person on the ground behind the car? 2.0 m/s. As you drive toward this parked car. Should the person jump out of the way? Account for your answer. The siren on the police car has a frequency of 860 Hz when the police car and the listener are stationary. A person standing in the middle of the street hears the horn with a frequency of 580 Hz.phy.za/courses/staffwebsites/wheaton/Teaching/teaching_index. its horn emits a frequency of 600 Hz. At what speed are you driving? 7. He notices that a police car has pulled up behind him and is matching his speed of 38 m/s. An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 90 km/hr. you observe the frequency to change by 95 Hz. A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25. but you hear the screech at 900 Hz. In which direction should you ride (toward or away from your friend) and at what minimum speed to know if the whistle is working? 4. Two train whistles. The siren of a fire engine that is driving northward at 30. A listener is between the two whistles and is moving toward the right with a speed of 15.htm Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 6 . You recall from biology that female hawks screech at 800Hz. To test it. and drive away. How fast is the hawk approaching? 3. What is the wavelength of the sound reaching your ears? 8. Suppose you are stopped for a traffic light. You suspect the whistle may not be working. 1. and an ambulance approaches you from behind with a speed of 18 m/s. a) What is the frequency from A as heard by the listener? b) What is the frequency from B as heard by the listener? 10. pass it.uct. When a car is at rest. A and B. A is stationary and B is moving toward the right (away from A) at a speed of 35. A truck in front of this fire engine is moving northward at 20. and then you hop on your bicycle.0 m/s. but your dog is ignoring it. What frequency does the speeder hear when the siren is turned on in the moving police car? 9.ac.Doppler Effect Exercises3 Unless otherwise stated take the speed of sound in air to be 340 m/s. The security alarm on a parked car goes off and produces a frequency of 960 Hz.0 m/s emits a sound of frequency 2000 Hz.0 m/s. but you can’t hear sounds above 20 kHz. a) What is the frequency of the siren’s sound that the fire engine’s driver hears reflected from the back of the truck? 3 http://www. What is the frequency heard by. The siren on the ambulance produces sound with a frequency of 955 Hz. A speeder looks in his rear-view mirror. A whistle you use to call your hunting dog has a frequency of 21 kHz. you ask a friend to blow the whistle.0 m/s. a) What frequency do you hear? b) What frequency does your friend hear if you suddenly start singing at 400 Hz? 5. each have a frequency of 444 Hz. Ultrasonic waves are emitted from the scan head and sent into the body of the patient. It has no known long-term side effects and rarely causes any discomfort to the patient. are used at frequencies from 20-40 kHz for jewelry.Additional resources: Ultra-Sound Ultrasound is sound with a frequency greater than the upper limit of human hearing. Interesting Fact: Ultrasound generator/speaker systems are sold with claims that they frighten away rodents and insects. making them useful for scanning the organs. such as dogs. watches. surgical instruments and industrial parts. dolphins. The scan head also acts a receiver for reflected waves. Typical ultrasound units have a hand-held probe (often called a scan head) that is placed directly on and moved over the patient: a water-based gel ensures good contact between the patient and scan head. have an upper limit that is greater than that of the human ear and can hear ultrasound. approximately 20 kilohertz. urology and endocrinology. controlled tests have shown that rodents quickly learn that the speakers are harmless. If the density decreases then the reflected waves has the same phase exactly like the case where the waves in a string were reflected from a free end. If the density increases then the reflected waves undergoes a phase shift exactly like the case where the waves in a string were reflected from a fixed end. where the operator can dynamically select the most useful section for diagnosing and documenting changes. the son of Gustav Ludwig Hertz. Ultrasonic waves are then sent into the fluid. Typical diagnostic ultrasound scanners operate in the frequency range of 2 to 13 megahertz. Uses Ultrasonography is widely utilized in medicine. but there is no scientific evidence that the devices work. • It shows the structure as well as some aspects of the function of organs. Ultrasound has industrial and medical applications. lenses and other optical parts. More powerful ultrasound sources may be used to generate local heating in biological tissue. often enabling rapid diagnoses. Strengths of ultrasound imaging • It images muscle and soft tissue very well and is particularly useful for finding the interfaces between solid and fluid-filled spaces. Medical ultrasonography can visualise muscle and soft tissue. who was a graduate student at the department for nuclear physics. Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 7 . Medical Ultrasonography Medical ultrasonography makes uses the fact that waves are partially reflected when the medium in which they are moving changes density. Interesting Fact: Medical ultrasonography was invented in 1953 at Lund University by cardiologist Inge Edler and Carl Hellmuth Hertz. with applications in physical therapy and cancer treatment. gynecology and obstetrics. and obstetric ultrasonography is commonly used during pregnancy. dental instruments. Ultrasonic cleaners. cardiology. Combining these properties of waves with modern computing technology has allowed medical professionals to develop an imaging technology to help with many aspects of diagnosis. The main mechanism for cleaning action in an ultrasonic cleaner is actually the energy released from the collapse of millions of microscopic cavitations events occurring in the liquid of the cleaner. primarily in gastroenterology. It is possible to perform diagnosis or therapeutic procedures with the guidance of ultrasonography (for instance biopsies or drainage of fluid collections). Some animals. These cleaners consist of containers with a fluid in which the object to be cleaned is placed. sometimes called supersonic cleaners. • It renders "live" images. Focused ultrasound sources may be used to break up kidney stones. From detailed knowledge of interference and refection an image of the internal organs can be constructed on a screen by a computer programmed to process the reflected signals. and bats. New York: Harper Collins College Publishers.G. The Free High School Science Texts: A Textbook for High School Students Studying Physics FHSST Authors. By calculating the frequency shift of a particular sample volume.phy. Pretoria: Aurora Drukpers.us/gbssci/phys/class/light/u12l2d. Brookes.A. its speed and direction can be determined and visualised. Patrick. OBE for FET Grade 12 Exam Study Guide Physical Sciences. sound. Conceptual Physical Science. d & Bowie.za/courses/staffwebsites/wheaton/Teaching/teaching_index. e. despite synthetic. P.nongnu. making it difficult to image structures that are far removed from the body surface. 1994. M. Weaknesses of ultrasound imaging • Ultrasound has trouble penetrating bone and performs very poorly when there is air between the scan head and the organ of interest. overlying gas in the gastrointestinal tract often makes ultrasound scanning of the pancreas difficult. Succhoki. which employ the Doppler effect to assess whether structures (usually blood) are moving towards or away from the probe.org/projects/fhsst Verleger. See http://savannah. New Yersey: Prentice Hall Gibbon. DC. For example. • Even in the absence of bone or air. Cape Town: Nasou Via Afrika Hewitt. the depth penetration of ultrasound is limited.uct.glenbrook.html http://www. Fisika. The Doppler information is displayed graphically using spectral Doppler. examinations can be performed at the bedside. http://www.• • • Equipment is widely available and comparatively °exible. H. Small. This is particularly useful in cardiovascular studies (ultrasonography of the vasculature and heart) and essential in many areas such as determining reverse blood flow in the liver vasculature in portal hypertension. especially in obese patients. • The method is operator-dependent. It is often presented audibly using stereo speakers: this produces a very distinctive.g. 1960. 1980. J.il. D. Doppler ultrasonography Ultrasonography can be enhanced with Doppler measurements. or as an image using colour Doppler or power Doppler. L. & Hewitt. Much cheaper than many other medical imaging technology. Physics. easily carried scanners are available. 2008.htm Dinaledi teacher training on grade 12 content: Module 2: DOPPLER EFFECT 8 .k12.ac. within a jet of blood flow over a heart valve. M.. BIBLIOGRAPHY Giancoli. A high level of skill and experience is needed to acquire good-quality images and make accurate diagnoses.
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