Physics
Doppler Effect
The Doppler Effect refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. This effect is commonly observed with sound waves, where the pitch of a sound appears to change as the source or observer moves. In astronomy, it is used to determine the motion of celestial bodies based on the shift in their spectral lines.
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eBook - ePub- 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 endIf 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 endIf 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.
eBook - ePubDiagnostic 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)
This causes the wave fronts travelling towards the observer to be more closely packed, so that the observer witnesses a higher frequency wave than that emitted. If, however, the source is moving away from the observer, the wave fronts will be more spread out, and the frequency observed will be lower than that emitted (Figure 7.1c). The resulting change in the observed frequency from that transmitted is known as the Doppler shift, and the magnitude of the Doppler shift frequency is proportional to the relative velocity between the source and the observer. Figure 7.1 Doppler Effect as a result of motion of the source (S) relative to a stationary observer (O). (a) There is no motion and the observer detects sound at a frequency equal to the transmitted frequency. (b) The source moves towards the observer and the observer detects sound at a higher frequency than that transmitted. (c) The source moves away from the observer and the observer detects a lower frequency than that transmitted. It does not matter whether the source or the observer is moving. If either one is moving away from the other, the observer will witness a lower frequency than that emitted. Conversely, if either the source or observer moves towards the other, the observer will witness a higher frequency than that emitted. Ultrasound can be used to assess blood flow by measuring the change in frequency of the ultrasound scattered from the moving blood. Usually the transducer is held stationary and the blood moves with respect to the transducer, as shown in Figure 7.2. The ultrasound waves transmitted by the transducer strike the moving blood, so the frequency of ultrasound as experienced by the blood is dependent on whether the blood is stationary, moving towards the transducer or moving away from the transducer. The blood then scatters the ultrasound, some of which travels in the direction of the transducer and is detected
eBook - ePubDigital 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 / fwhere 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.
eBook - ePub- 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 , wheref D = the Doppler frequencyf 0 = the transmitted ultrasound frequencyv = the reflector (blood) velocityc = the speed of soundcosine 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
eBook - ePub- 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.
eBook - ePub- 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
eBook - ePub- 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 MODEThe 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
Similarly, the scattered field is expressed asE r(=r , t)Er 0ei ()ω it −⋅k →ir →(11.5) E s(=r , t)Es 0ei ()ω st −⋅k →sr →(11.6) where ωs == ωi + μV (2π/λ)sin θ for the geometry given in Figure 11.2ω i+ μV →⋅()−k →sk →i
eBook - ePub- Raghbir Singh Khandpur(Author)
- 2019(Publication Date)
- Wiley(Publisher)
The backscattered Doppler‐shifted signals from a blood vessel range in intensity from 50 dB to more than 120 dB down from the transmitted signal. The receivers designed for this purpose have a bandwidth of 3 MHz and gain in excess of 80 dB. This is followed by a single sideband‐type quadrature phase detector, which separates the upper and lower Doppler sidebands for sensing flow direction. The detector consists of a phase‐shift network, which splits the carrier into two components that are in quadrature, which means they are at 90°. These reference cosine and sine waves must be several times larger than the RF amplifier output. The Doppler shift of the received echo, backscattered by the moving blood, is detected by sensing the instantaneous phase difference between the echo and a reference signal from the master oscillator. If the echo at a particular range or depth contains a Doppler shift, then the amplitude of a sample of the instantaneous phase difference will vary in amplitude exactly with the Doppler difference frequency. The envelope frequency from the phase detector is the Doppler difference frequency.If the flow of blood is in the same direction as the ultrasonic beam, then it is considered that the blood is flowing away from the transducer. In this case, the Doppler shift frequency is lower than that of the carrier, and the phase of the Doppler wave lags behind that of the reference carrier. If the flow of blood is towards the transducer, then the Doppler frequency is higher than the carrier frequency and the phase of the Doppler wave leads the reference carrier. Thus, by examining the sign of the phase, the direction of flow can be established.The depth at which the Doppler signal is sensed within the blood vessel and tissue depends on the delay interval between the transmitted burst and the sample gate. For a velocity of sound, in tissue of approximately 1500 m/s, the range factor is 13.3 μs delay/cm of depth. A one‐shot multi‐vibrator is used to develop the adjustable range delay calibrated in millimetres of depth. This is followed by a ‘sample gate’. The detected Doppler shift frequency will correspond to the mean velocity averaged over the sample volume. However, the Doppler signals at the output of the sample and hold circuit are low in amplitude and contain frequency components from the transmitter pulse repetition rate and the low frequency large amplitude signals produced by the motion of interfaces such as vessel walls and the myocardium. Therefore, both high pass and low pass filters are used to extract the signals of interest. Once the signals are filtered with a passband of 100 Hz–5 kHz, it is further amplified to drive an external audio amplifier or a frequency meter.
