Doppler's Effect

INTRODUCTION

Doppler Effect or Doppler Shift

Christian Doppler was an Austrian mathematician who lived between 1803-1853. He is known for the principle he first proposed in Concerning the coloured light of double stars in 1842. This principle is now known as the Doppler Effect. He hypothesized that the pitch of a sound would change if the source of the sound was moving.

¨  named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague. 

¨  Is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

The relative increase in frequency can be explained as follows. When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the observer than the previous wave. Therefore each wave takes slightly less time to reach the observer than the previous wave. Therefore the time between the arrivals of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wavefronts is reduced; so the waves "bunch together".

DOPPLER’S EFFECT

¨  The Doppler effect causes the received frequency of a source (how it is perceived when it gets to its destination) to differ from the sent frequency if there is motion that is increasing or decreasing the distance between the source and the receiver. This effect is readily observable as variation in the pitch of sound between a moving source and a stationary observer. Imagine the sound a race car makes as it rushes by, whining high pitched and then suddenly lower. Vrrrm-VROOM. The high pitched whine is caused by the sound waves being compacted as the car approaches you, the lower pitched VROOM comes after it passes you and is speeding away. The waves are spread out.

By analogy, the electromagnetic radiation emitted by a moving object also exhibits the Doppler effect. The radiation emitted by an object moving toward an observer is squeezed; its frequency appears to increase and is therefore said to be blueshifted. In contrast, the radiation emitted by an object moving away is stretched or redshifted. As in the ambulance analogy, blueshifts and redshifts exhibited by stars, galaxies and gas clouds also indicate their motions with respect to the observer.

¨  When the distance between the source and receiver of electromagnetic waves remains constant, the frequency waves is the same in both places. When the distance between the source and receiver of electromagnetic waves is increasing, the frequency of the received wave forms is lower than the frequency of the source wave form. When the distance is decreasing, the frequency of the received wave form will be higher than the source wave form.

Besides sound and radio waves, the Doppler effect also affects the light emitted by other bodies in space. If a body in space is "blue shifted," its light waves are compacted and it is coming towards us. If it is "red shifted" the light waves are spread apart, and it is traveling away from us. All other stars we have detected are "red shifted," which is one piece of evidence for the theory that the universe is constantly expanding, perhaps from a "big bang."

So far we have only discussed cases where the source of waves is at rest. Often, waves are emitted by a source that moves with respect to the medium that carries the waves, like when a speeding cop car blares its siren to alert onlookers to stand aside. The speed of the waves, v, depends only on the properties of the medium, like air temperature in the case of sound waves, and not on the motion of the source: the waves will travel at the speed of sound (343 m/s) no matter how fast the cop drives. However, the frequency and wavelength of the waves will depend on the motion of the wave’s source. This change in frequency is called a Doppler shift.Think of the cop car’s siren, traveling at speed , and emitting waves with frequency f and periodT = 1/f. The wave crests travel outward from the car in perfect circles (spheres actually, but we’re only interested in the effects at ground level). At time T after the first wave crest is emitted, the next one leaves the siren. By this time, the first crest has advanced one wavelength, , but the car has also traveled a distance of . As a result, the two wave crests are closer together than if the cop car had been stationary.

The shorter wavelength is called the Doppler-shifted wavelength, given by the formula . 

The Doppler-shifted frequency is given by the formula:

Similarly, someone standing behind the speeding siren will hear a sound with a longer wavelength, 

, and a lower frequency,

 .

You’ve probably noticed the Doppler effect with passing sirens. It’s even noticeable with normal cars: the swish of a passing car goes from a higher hissing sound to a lower hissing sound as it speeds by. The Doppler effect has also been put to valuable use in astronomy, measuring the speed with which different celestial objects are moving away from the Earth.

EXAMPLE

A cop car drives at 30 m/s toward the scene of a crime, with its siren blaring at a frequency of 2000 Hz. At what frequency do people hear the siren as it approaches? At what frequency do they hear it as it passes? The speed of sound in the air is 343 m/s.

As the car approaches, the sound waves will have shorter wavelengths and higher frequencies, and as it goes by, the sound waves will have longer wavelengths and lower frequencies. More precisely, the frequency as the cop car approaches is:

The frequency as the cop car drives by is:

Development

Doppler first proposed the effect in 1842 in his treatise "ber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmes" (On the coloured light of the binary stars and some other stars of the heavens). Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but was not adopted by the rest of the world as Fizeau's discovery was three years after Doppler's; therefore, it was only an addition to a previously established discovery).

Application

Sirens

The siren on a passing emergency vehicle will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer.

As the ambulance approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch. As the ambulance recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the ambulance is coming nearer or speeding away.

Astronomy

Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left).

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blue shift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us, that is, the radial velocity. This is used to detect if an apparently single star is, in reality, a close binary and even to measure the rotational speed of stars and galaxies.

The use of the Doppler effect for light in astronomy depends on our knowledge that the spectra of stars are not continuous. They exhibit absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blue shift and those of a receding astronomical light source exhibit a redshift.

           Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and -260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.

Temperature Measurement

Another use of the Doppler effect, which is found mostly in plasma physics and astronomy, is the estimation of the temperature of a gas (or ion temperature in a plasma) which is emitting a spectral line. Due to the thermal motion of the emitters, the light emitted by each particle can be slightly red- or blue-shifted, and the net effect is a broadening of the line. This line shape is called a Doppler profile and the width of the line is proportional to the square root of the temperature of the emitting species, allowing a spectral line (with the width dominated by the Doppler broadening) to be used to infer the temperature.

Radar

The Doppler effect is used in some types of radar, to measure the velocity of detected objects. A radar beam is fired at a moving target — e.g. a motor car, as police use radar to detect speeding motorists — as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's velocity. Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar to explode at the correct time, height, distance, etc.

Medical Imaging and Blood Flow 

Measurement

An echocardiogram can, within certain limits, produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output. Contrast-enhanced ultrasound using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.

Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).

Velocity measurements of blood flow are also used in other fields of medical ultrasonography, such as obstetric ultrasonography and neurology. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like stenosis.

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. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency.

Velocity Profile Measurement

Developed originally for velocity measurements in medical applications (blood flows), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive.

Underwater Acoustics

In military applications the Doppler shift of a target is used to ascertain the speed of a submarine using both passive and active sonar systems. As a submarine passes by a passive sonobuoy, the stable frequencies undergo a Doppler shift, and the speed and range from the sonobuoy can be calculated. If the sonar system is mounted on a moving ship or another submarine, then the relative velocity can be calculated.

Audio

The Leslie speaker, associated with and predominantly used with the Hammond B-3 organ, takes advantage of the Doppler Effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note.

Vibration Measurement

A laser Doppler vibrometer (LDV) is a non-contact method for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.

The Doppler’s Effect video

ENRICHMENT

       1. A mass is executing simple harmonic motion with amplitude A. What is the total distance traveled by the mass during one period of the oscillation? Does your answer depend on the time instant from which the period of the oscillation is measured?

Answer:

During one complete oscillation, the mass travels a distance of 4A.

Where the cycle is deemed to start does not matter.

    2. The following diagram depicts a series of straight waves traveling from shallow water into deeper water. Complete the diagram by drawing in the following:
(a) incident ray; (b) reflected ray; (c) refracted ray; (d) two refracted wave fronts; (e) two reflected wave fronts.

Answer: 

    3. The security alarm on a parked car goes off and produces a frequency of 735 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 78.4 Hz. At what speed are you driving?

Answer:

The change in frequency can be calculated using the general Doppler equation:

f'=f((V+-Vo) / (V-+Vs))

V is speed of sound (343m/s)

Vo is speed of observer

Vs is speed of source

f' is shifted frequency

f is original frequency

f'=f((V+Vo)/(V-Vs)) used for situations in which the source and the observer are coming closer together

f'=f((V-Vo)/(V+Vs)) used for situations that they are moving away from one another.

So for this question, when you drive toward this parked car

f'1=735*(343+Vo)/343

when you drive away

f'2=735*(343-Vo)/343

The difference in f' will be 735*2*Vo/343=78.4 , solve this one gives the speed of observer

Vo=18.29m/s=65.86km/hr

   4. Transverse waves traveling across a rope have a frequency of 12.0 Hz and a wavelength of 2.40 m. What is the velocity of the waves?

Answer:

The universal wave equation applies:

v = λf where v = the speed of propagation, λ = wavelength, and f = frequency.

v = λf = (12)(2.40) = 28.8 m/s

ASSESSMENT

1.       During the Doppler shift, approaching sound waves __________.

a.      Lengthen

b.      Shorten

c.       Gain amplitude

d.      Decrease frequency

2.       When a train passes and its whistle sounds like it changes pitch, the cause is __________.

a.     The Doppler effect

b.    The Big Bang

c.     The Galileo effect

d.    Speed change

3.       Due to the Doppler effect, the _____ of a sound increases as the source approaches you.

a.     Amplitude

b.    Speed

c.     Wavelength

d.    Sound level

4.      For waves that propagate in a medium, such as ________ waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted.

a.    Waves

b.    Sounds

c.    Doppler effect

d.    Interference

5.       In Britain, ________ made an experimental study of the Doppler effect (1848).

a.    Jonh Scott Russel

b.    Alexander Graham Bell

c.    Edward Jener

d.    Daniel Bernoulli

6.      The Doppler effect is used in some types of ________, to measure the velocity of detected objects.

a.    Sounds

b.    Waves

c.    Radar

d.    Siren

7.       One of the limitations is that the ________ beam should be as parallel to the blood flow as possible.

a.    Ultra waves

b.    Ultrasounds

c.    Doppler

d.    Radar

8.      If the sonar system is mounted on a moving ship or another submarine, then the relative ________ can be calculated.

a.    Kinematics

b.    Velocity

c.    Speed

d.    Classical mechanics

9.      It has been used to measure the speed at which stars and ________ are approaching or receding from us, that is, the radial velocity.

a.    Galaxy

b.    Milky way

c.    Andromeda galaxy

d.    Spiral galaxy

10.   For waves which do not require a medium, such as light or gravity in ________, only the relative difference in velocity between the observer and the source needs to be considered.

a.    General relatively

b.    Black hole

c.    Gravitation

d.    Sound