Doppler Effect in Light

8 Key excerpts on "Doppler Effect in Light"

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  eBook - ePub

  Digital Signal Processing 101

  Everything You Need to Know to Get Started

  • Michael Parker(Author)
  • 2017(Publication Date)
  • Newnes

    (Publisher)

  By measuring the Doppler rate, the radar is able to measure the relative velocity of all objects returning echoes to the radar system—whether planes, vehicles, or ground features. For targeting radars, estimating the targets' velocity is equally important as determining its location. And for all radars, Doppler filtering can be used to discriminate between objects moving at different relative velocities. This can be especially important when there is a high level of clutter obscuring the target return. An example of this might be an airborne radar trying to track a moving vehicle on the ground. Since the ground returns will be at the same range as the vehicle, the difference in velocity will be the means of discrimination using Doppler measurements.

  19.1. Doppler Effect

  Because sensing Doppler frequency shifts is so important, it is worth reviewing the cause of Doppler frequency shifts. A common example we have all experienced is standing beside a train track or highway. As a train or truck approaches, we hear a certain frequency sound. As a high speed train or truck passes, the sound immediately drops several octaves. This is caused by a frequency shift caused by the Doppler effect. Although we cannot sense this, the light waves are affected in the same way as sound waves. In fact, the realization that our universe is expanding was determined by making very fine Doppler measurements of the light from stars in the night sky.

  The relationship between wavelength and frequency is as follows:

  λ =

  v / f

  where f  =  wave frequency (Hz or cycles per second), λ  =  wavelength (meters), v  =  speed of light (approximately 3  ×  108   m/s).

  The speed of light is constant—Einstein proved this. Technically this is true only in a vacuum, but the effect of the medium such as our atmosphere can be ignored in radar discussions. What is happening in a radar system is that the frequency is modified by the process of being reflected by a moving object. Consider the transmission of a sinusoidal wave. The distance from the crest of each wave to the next is the wavelength, which is inversely proportional to the frequency. Each successive wave is reflected from the target object of interest. When this object is moving toward the radar system, the next wave crest reflected has a shorter round-trip distance to travel, from the radar to the target and back to the radar. This is because the target has moved closer in the interval of time between the previous and current wave crest. As long as this motion continues, the distance between the arriving wave crests is shorter than the distance between the transmitted wave crests. Since frequency is inversely proportional to wavelength, the frequency of the sinusoidal wave appears to have increased. If the target object is moving away from the radar system, then the opposite happens. Each successive wave crest has a longer round-trip distance to travel, so the time between arrival of receive wave crests is lengthened, resulting in a longer (larger) wavelength and a lower frequency. This effect becomes more pronounced when the frequency of the transmitted sinusoid is high (short wavelength). Then the effect of the receive wavelength being shorted or lengthened due to the Doppler effect is more noticeable. Therefore, Doppler frequency shifts are more easily detected when using higher frequency waves, as the percentage change in the frequency will be larger.

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  Biophysics For Dummies

  • Ken Vos(Author)
  • 2013(Publication Date)
  • For Dummies

    (Publisher)

  Doppler Effect is the name given to the phenomenon of the frequency of a wave changing when the source of the wave or the observer is in motion. Imagine you’re at the beach. If you’re just standing in the water, the crests of waves will hit you with some frequency, but if you’re walking into the waves, they’ll hit you at a faster rate. Many fields of science including biophysics use the Doppler Effect; even some animals have evolved to take advantage of it.

  The following sections explain why the Doppler Effect occurs by first looking at the listener moving, then the source moving, and finally when both the source and the listener are moving. These sections also introduce the Doppler Effect for electromagnetic radiation (light) because the behavior is slightly different for light.

  Moving on the receiver’s end

  If the source of the wave is stationary and the receiver is moving (vreceiver ), then the frequency at the receiver (freceiver ) will change relative to the frequency originally produced (fsource ):

  The minus sign is if the receiver is moving away from the source, and the plus sign is for when the receiver is moving toward the source. This modification to the frequency occurs because the distance between the crests (the wavelength) is unchanged, but because the receiver is moving, it will take longer (if it’s moving away from the source) or less time (if it’s moving toward the source) for each crest to reach the receiver.

  Moving on the source’s end

  If the source of the wave is moving (vsource ) and the receiver is stationary, then the frequency received (freceiver ) will change relative to the frequency originally produced (fsource ) as such:

  The plus sign is if the source is moving away from the receiver, and the minus sign is for when the source is moving toward the receiver. This modification to the frequency occurs because the distance between the crests is shrunk in the direction the source is moving, whereas the distance between the crests is stretched in the direction opposite to the direction the source is moving.

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  100 Science Discoveries That Changed the World

  • Colin Salter(Author)
  • 2021(Publication Date)
  • Pavilion

    (Publisher)

  It was a train which first demonstrated the audio Doppler Effect, three years after Doppler’s publication which focused on light waves. Noted Dutch chemist Buys Ballot employed a small brass band to travel on the Utrecht to Amsterdam railway line and play a single constant note. He measured its pitch as the train approached, passed and receded from him and confirmed that Doppler’s theory worked as well for waves of sound as of light.

  Christian Doppler was born in Salzburg, Austria, in a house adjacent to a former residence of the Mozart family.

  For most of us the Doppler Effect is just a curiosity associated with the passing of fire engine sirens. For science, however, Doppler’s explanation is of profound interest in many fields of study. It has been shown to apply to electromagnetic waves too, and in astronomy the phenomena of red shift and blue shift are explained by rises and falls respectively of electromagnetic frequencies.

  The effect can also be exploited in the use of radio waves, for example in the control of mobile robots, or in communication with fast-moving satellites. Radar waves fired from police speed guns take the Doppler Effect into account when calculating the speed of a receding vehicle.

  The Doppler Effect has applications in medical science too. An ultrasound scan of the heart, an echocardiogram, makes use of it to determine the direction and volume of blood flow, a useful tool for early diagnosis of cardiovascular problems.

  An ultrasound image of the heart using the Doppler mode.

  The Zillertalbahn mountain railway in the Austrian Tyrol.

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  Diagnostic Ultrasound, Third Edition

  Physics and Equipment

  • Peter R Hoskins, Kevin Martin, Abigail Thrush, Peter R Hoskins, Kevin Martin, Abigail Thrush(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Multiple Choice Questions

  Q1. The Doppler effect is the change in due to the relative motion of source and observer.

  a. Speed of sound

  b. Velocity of sound

  c. Frequency

  d. Amplitude

  e. Wavelength

  Q2. If a source emits sound of frequency f , an observer moving to the source will experience:

  a. Sound of a higher frequency than f

  b. Sound that is the same frequency as f

  c. Sound of a lower frequency than f

  d. Sound with two frequencies, one at f and one at twice f

  e. No sound

  Q3. If a source emits sound of frequency f , an observer stationary with respect to the source will experience:

  a. Sound of a higher frequency than f

  b. Sound that is the same frequency as f

  c. Sound of a lower frequency than f

  d. Sound with two frequencies, one at f and one at twice f

  e. No sound

  Q4. Ultrasound is generated at a frequency f . If blood moves away from the transducer the frequency of the received echoes will:

  a. Be lower than f

  b. Be higher than f

  c. Be the same as f

  d. Consist of two frequencies at f and f /2

  e. There will be no received echoes

  Q5. In Doppler ultrasound the Doppler shift is:

  a. The difference in wavelength between the transmitted ultrasound and received ultrasound

  b. The difference in frequency between the transmitted ultrasound and received ultrasound

  c. The difference in amplitude between the transmitted ultrasound and received ultrasound

  d. The difference in speed of sound between the transmitted ultrasound and received ultrasound

  e. The difference in angle theta between the transmitted ultrasound and received ultrasound

  Q6. In Doppler ultrasound the Doppler shift is:

  a. Proportional to the speed of sound

  b. Inversely proportional to the velocity of the target

  c. Proportional to the square of the velocity of the target

  d. Proportional to the velocity of the target

  e.

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  AAGBI Core Topics in Anaesthesia 2012

  • Ian Johnston, William Harrop-Griffiths, Leslie Gemmell, Ian Johnston, Leslie Gemmell, William Harrop-Griffiths(Authors)
  • 2011(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  In 1842, Christian Andreas Doppler used the changing frequency of light from the stars to calculate their speed of movement, and later applied this to sound. The phenomenon can be illustrated by the change in the sound of the whistle of an approaching train. When the origin of a sound wave is approaching the hearer, the wavelength shortens and the pitch is higher. As the origin of the sound goes away from the hearer, the sound wave lengthens and the pitch falls. In terms of physics, the approaching waves are compressed and the receding waves have a longer wavelength. This perceived change in frequency is called Doppler shift. In the case of ultrasound waves, which are being emitted and detected by the same transducer:

  • If the object is moving towards the source of the ultrasound, then the wavelength becomes shorter.
  • If the object is moving away, the wavelength becomes longer.

  The Doppler frequency is the difference between the frequency of the emitted ultrasound and that of the received echo. By measuring the change in frequency, the direction and speed of movement can be calculated. If the probe and ultrasound waves are at right angles to the blood vessel, the layers of the blood vessel wall will produce an image but once the waves are in the blood, scatter will occur and a homogeneous image is created; there is no Doppler shift. However if the probe and sound waves are at an angle to the flow of blood, a change in frequency in any waves that have been scattered and return to the probe will be detected. The change of frequency is given by:

  f D = 2 f 0 v cosine θ / c , where

  f D = the Doppler frequency

  f 0 = the transmitted ultrasound frequency

  v = the reflector (blood) velocity

  c = the speed of sound

  cosine θ = the cosine of the angle between the transmitter beam and the reflector pathway.

  The cosine of 90° is 0, so if the beam is at right angles to the flow, no shift in wavelength will occur. In practice, the perpendicular beam that produces the best B mode images produces no signal for flow and makes it impossible to measure the velocity of a moving object. An incident angle of 30–60° to the vessel lumen gives the best angle to estimate the velocity. The Doppler beam steer alters the angle of the Doppler beam. The angle correction

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  eBook - ePub

  Diagnostic Ultrasound Imaging: Inside Out

  • Thomas L. Szabo(Author)
  • 2013(Publication Date)
  • Academic Press

    (Publisher)

  θ ,

  (11.1A)

  and solving for the Doppler frequency (f D ) in terms of the transmitted frequency (f 0 ),

  (11.1B)

  leads to a Doppler shift, correct to first order when c s =c 0 ,

  (11.1C)

  Figure 11.1 Doppler-shifted wave frequencies from a moving source as seen by observers at different locations.Observers at (A) 0°, (B) 90°, (C) 180°, (D) 270°, and (E) 45° angles relative to the directions of the source.

  From this equation, the perceived frequencies for the observers in Figure 11.1 can be calculated for a 10-kHz source tone moving at a speed of 100 km/hr (v =27.78 m/s) in air (c 0 =330 m/s). Observers B and D, at 90° to the source vector, hear no Doppler shift. Observer A detects a frequency of 10,920 Hz, while observer C (here, θ =π ) hears 9,220 Hz.

  A similar argument yields an equation for a stationary source and a moving observer with a velocity c obs ,

  (11.2)

  The Doppler effect plays with our sense of time, either expanding or contracting the timescale of waves sent at an original source frequency (f 0 ). Furthermore, it is important to bear in mind the bearing or direction of the sound relative to the observer in terms of vectors.

  Now consider a flying bat intercepting a flying mosquito based on the Doppler effect caused by the relative motion between them (see Figure 11.2 ). It is straightforward to show that if the mosquito source has a speed of c s , and the bat has a speed of c obs

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  Introduction to Optical Metrology

  • Rajpal S. Sirohi(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  14 Hz. Thus, the Doppler shift is a very small fraction of the frequency of the incident wave and hence direct measurement of the Doppler shift introduces large uncertainties in its measurement and consequently in the determination of velocity. Hence the Doppler frequency is measured by heterodyning: the scattered light is mixed with the direct light. There are a number of methods based on heterodyning, which are explained below.

  11.2.1  REFERENCE BEAM MODE

  The light scattered by the moving scatterer is mixed with that of the unscattered light on a photodetector. The output of the detector is a Doppler signal. Figure 11.2 shows the schematic of the experimental setup. Beam from a laser is divided into two beams: the illumination and the reference beams. The illumination beam, which is stronger than the reference beam, is focused at a point of interest in the flow field.

  FIGURE 11.2  A schematic of the reference beam mode to measure flow velocity.

  The reference beam need not pass through the flow field but must be collinear with the scattered beam. A mask selects the direction. These two beams then mix at the photodetector say a photomultiplier tube (PMT). The signal from the PMT is processed to obtain velocity.

  Let the reference beam be expressed by

  E r ( r , t )   =   E r 0 e i ( ω i t   −   k → i   ⋅   r → )

  (11.5)

  Similarly, the scattered field is expressed as

  E s ( r , t )   =   E s 0 e i ( ω s t   −   k → s   ⋅   r → )

  (11.6)

  where ωs =

  ω i

    +   μ

  V →

    ⋅  

  (

  k →

  s

    −  

  k →

  i

  )

  = ωi + μV (2π/λ)sin θ for the geometry given in Figure 11.2

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  The Special Theory of Relativity

  • David Bohm(Author)
  • 2015(Publication Date)
  • Routledge

    (Publisher)

  The more modern and very exact measurements of the velocity of light by the equivalent of the Fizeau method, as discussed in Chapter 7, depend on the combination of the Lorentz contraction and the change of periods of clocks. Since the Lorentz transformation itself is already checked by the Michelson–Morley experiment, we may regard the Fizeau method as confirming the variation of the rates of clocks, with their velocity, as predicted by the Lorentz transformation. However, there exists more direct verification of the variation of the rate of clocks. Thus in Chapter 16 we have discussed the observations on the mean time decay of rapidly moving mesons and the Doppler shift for light viewed perpendicular to the direction of motion of the source, both of which have provided very accurate confirmation of the predictions of the Lorentz transformation concerning the increase of period that should be observed for moving clocks. The direct experimental confirmation of the remaining prediction concerning the nonsimultaneity of separated clocks is rather more difficult to obtain. At first sight it would seem that one could test this by considering the relativistic law for the addition of velocities (15–7) and (15–8), the derivation of which depended on the formula (15–6), expressing just the property of nonsimultaneity of such clocks that is under discussion. This law has been quite accurately confirmed, for example, by the measurement of the speed of light in flowing water, described in Chapter 17. Unfortunately, such a test is not unambiguous in its significance, because, as can be shown (see, for example, C. C. Moller, The Theory of Relativity) nonrelativistic theories of electromagnetic phenomena can be made to give the same results as relativistic theories to the order of the experiments that are available

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