The Doppler effect

The Doppler effect is used in practice to visualize directional blood flow on ultrasound, to estimate cardiac output and in some types of flow meter. 

The phenomenon by which the frequency of transmitted sound is altered as it is reflected from a moving object. It is represented by the following equation  

Sound waves are emitted from the probe (P) at a frequency F0. They are reflected off moving red blood cells and back towards the probe at a new frequency, FR. The phase shift can now be determined by FR-F0. The angle of incidence (9) is shown on the diagram. If a measurement or estimate of the cross-sectional area of the blood vessel is known, flow can be derived as area multiplied by velocity (m2.m.s 1 = m3.s 1). This is the principle behind oesophageal Doppler cardiac output monitoring. 

It is also possible to calculate the pressure gradients across heart valves using the Doppler principle to measure the blood velocity and entering the result into the Bernoulli equation. 

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High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Whether radiation is being absorbed or emitted the frequency at which it takes place depends on the velocity of the atom or molecule relative to the detector. This is for the same reason that an observer hears the whistle of a train travelling towards him or her as having a frequency apparently higher than it really is, and lower when it is travelling away from him or her. The effect is known as the Doppler effect. 

Identification of a molecule known in the laboratory is usually unambiguous because of the uniqueness of the highly precise transition frequencies. However, before frequencies detected in the interstellar medium can be compared with laboratory frequencies they must be corrected for the Doppler effect (see Section 2.3.2) due to the motion of the clouds. In Sagittarius B2 the molecules are found to be travelling fairly uniformly with a velocity of... 

J. Stark (Greifswald) discovery of the Doppler effect on canal rays and of the splitting of spectral lines in electric fields. 

Microwave movement detectors utilize the principle of the Doppler effect on high-frequency low-power radio waves. These units are moderate in cost and suitable for large-volume coverage. Microwaves, however, penetrate certain materials easily, such as plasterboard, and careful siting is required to avoid false alarms. 

Ultrasonic movement detectors utilize the principle of the Doppler effect on high-frequency sound waves. Ultrasonic movement detectors do not penetrate solid objects, but have smaller volume of coverage than microwave movement detectors. These units may also be affected by moving hot or cold air pockets in a room. 

Figure 4.16. To cover all possible transitions in the absorbing nucleus, the energy of the source radiation is modulated by using the Doppler effect, such that the emitted radiation has an energy E v) = Eo(l + vjc). For Fe the required velocities fall in the range (1 to t-1 cm s k In Mossbauer emission spectroscopy, the sample under investigation is the source, and a single line absorber is...

In an actual Mdssbauer transmission experiment, the radioactive source is periodically moved with controlled velocities, +u toward and —d away from the absorber (cf. Fig. 2.6). The motion modulates the energy of the y-photons arriving at the absorber because of the Doppler effect Ey = Eq + d/c). Alternatively, the sample may be moved with the source remaining fixed. The transmitted y-rays are detected with a y-counter and recorded as a function of the Doppler velocity, which yields the Mdssbauer spectrum, r(u). The amount of resonant nuclear y-absorption is determined by the overlap of the shifted emission line and the absorption line, such that greater overlap yields less transmission maximum resonance occurs at complete overlap of emission and absorption lines. 

Mossbauer spectra are usually recorded in transmission geometry, whereby the sample, representing the absorber, contains the stable Mossbauer isotope, i.e., it is not radioactive. A scheme of a typical spectrometer setup is depicted in Fig. 3.1. The radioactive Mossbauer source is attached to the electro-mechanical velocity transducer, or Mossbauer drive, which is moved in a controlled manner for the modulation of the emitted y-radiation by the Doppler effect. The Mossbauer drive is powered by the electronic drive control unit according to a reference voltage (Fr), provided by the digital function generator. Most Mossbauer spectrometers are operated in constant-acceleration mode, in which the drive velocity is linearly swept up and down, either in a saw-tooth or in a triangular mode. In either case. 

In this section, the relationship between the measured quantity and the desired center-of-mass differential cross-section will be established and a brief description of the data analysis procedure will then be given. First, consider a Newton sphere with a single value of the product velocity v (see Fig. 4). From the Doppler-shift formula, at a given laser wavelength, the Doppler effect selectively ionizes those ions with vz = vcosO in the... 

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

Now we consider the possibility that the target is moving relative to the radar. The scattered waveform is modified by the Doppler effect. If this is done correctly it results in a time dilation of the return signal, so that, if the target has a radial velocity v, the return signal su(t) becomes... 

Mossbauer spectroscopy The Mossbauer effect is resonance absorption of 7 radiation of a precisely defined energy, by specific nuclei. It is the basis of a form of spectroscopy used for studying coordinated metal ions. The principal application in bioinorganic chemistry is Fe. The source for the 7 rays is Co, and the frequency is shifted by the Doppler effect, moving it at defined velocities (in mm/s) relative to the sample. The parameters derived from the Mossbauer spectrum (isomer shift, quadrupole splitting, and the hyperfine coupling) provide information about the oxidation, spin and coordination state of the iron. 

Doppler spectroscopy spect A technique for measuring the speed with which an object is moving toward or away from the observer by measuring the amount that light from the object is shifted to a higher or lower frequency by the Doppler effect. dap-l3r spek tras-ko-pe)... 

In terms of the Doppler effect [discovered in 1842 by -C. Doppler (1803-1853)], the frequency of the voltage from the crystal detector can be considered as the Doppler shift in frequency f given by... 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

Linewidth is also affected by pressure broadening from collisions between atoms. Collisions shorten the lifetime of the excited state. The uncertainty in the frequency of atomic absorption and emission lines is roughly numerically equal to the collision frequency between atoms and is proportional to pressure. The Doppler effect and pressure broadening are similar in magnitude and yield linewidths of 10-3 to I0-2 nm in atomic spectroscopy. 

Figure 21-15 The Doppler effect. A molecule moving (a) toward the radiation source feels the electromagnetic field oscillate more often than one moving (to) away from the source.

Explain what is meant by the Doppler effect. Rationalize why Doppler broadening increases with increasing temperature and decreasing mass in Equation 21-5. 

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