The Doppler Effect And Its Applications

Perhaps you have noticed how the sound of a vehicle’s horn changes as the vehicle moves past you. The frequency of the sound you hear as the vehicle approaches you is higher than the frequency you hear as it moves away from us. This is one example of the Doppler Effect. To see what causes this apparent frequency change, imagine you are in a boat that is lying at anchor on a gentle sea where the waves have a period of T =30s. This means that every 3.0 s a crest hits your boat. These effects occur because the relative speed between your boat and the waves depends on the direction of travel and on the speed of your boat. When you are moving toward the right in Figure 17.9b, this relative speed is higher than that of the wave speed, which leads to the observation of an increased frequency. When you turn around and move to the left, the relative speed is lower, as is the observed frequency of the water waves.

Content

Doppler Effect (Sound) and its Application

Introduction

In physics, the Doppler Effect can be defined as, “The increase or decrease in the frequency of sound and also to other waves such as the source and observer moving toward or away from each other. Thus the effect causes the change in pitch which is clearly noticed in a passing siren or train horn, as well as in the red shift/blue shift.

The Doppler Effect is familiar to us with everyday experiences. It explains us the change in the pitch of a fast moving car horn or any other fast moving sound source as it passes us. If the car is approaching us, the pitch of the car’s horn will be greater than if the car were stationary and as the car passes us and begins to move away from us the pitch will be lower than if the car were stationary. In fact, whenever the source and observer of a sound are in relative motion, the observed frequency will be different than that of the emitted one by the source.

For example:

The Observer feel higher frequency, when the train is coming to the observer.

The Observer feel lower frequency, when the train is going far from the observer.

History:

The Doppler Effect was discovered by a scientist named Christian Doppler, who gifted his idea to us in year1842. He thought, “if sound wave coming from the source might have a greater frequency and if the source is moving toward or the observer so there will be lower frequency if the source is moving away from the observer. Though some doubted the existence of this phenomenon, it was experimentally verified in 1845 by C. H. D. Buys Ballot (1817-1890) of Holland. Buys Ballot examined the alteration in pitch as he was passed by a locomotive carrying several trumpeters, all playing a constant note. The Doppler effect is considered most often in relation to sound (acoustic waves) and light (electromagnetic waves) but holds for any wave. When the source and observer of light waves move apart, the observed light will be shifted to lower frequencies, towards the “red” end of the spectrum, while if the source and observer move toward each other the light will be shifted to higher frequencies, towards the “blue” end of the spectrum.

The Doppler Effect is the phenomenon to observe at a particular time when the wave is emitted by a source moving w.r.t. the observer .The Doppler Effect can be stated as the effect produced by a moving source of wave when there is an apparent upward shift in the frequency to be observed by the observer and the source which is approaching toward it and the downward shift in the frequency to which it when the observer and the source is contacting.

Change in the wavelength due to the motion of the source

For the waves which propagate in the medium, such as sound waves, the speed of the observer and the source are in relation with the medium to which the waves are transmitted. The Doppler Effect may result from the change in position of the source, relative motion to the observer. Each of the effect is analyzed singly. For the waves which do not require any medium for propagation, eg. Light and gravity in general relativity, for it the difference in velocity of the observer and that of the source needs to be considered.

HOW DOPPLER EFFECT DOES OCCURS:

TYPES OF DOPPLER EFFECT:

Symmetrical: – It implies that Doppler shift is same when the source of light moves towards/away from a stationary observer or the observer moves with the same velocity towards/away from the stationary source.

Asymmetrical: – It implies that apparent change in the frequency is different when the source of sound moves towards/away from a stationary observer or as that occurs, when the observer moves with the same velocity towards/away from the stationary source.

DOPPLER FORMULAE:

Now the observer is in motion and also the source is stationary, then the measured frequency is:

(1)

When the up sign correspond to the arriving observer and the lower sign correspond to a receding observer.

Now the source is in motion and the observer is stationary, then the measured frequency is:

, (2)

Where the up sign correspond to the source arriving and the lower sign correspons to the source receding from the observer.

When both the source and observer are in motion, then the measured frequency is:

3)

Note that the sign in the numerator and denominator are not depending on each other. By using the general facts for the sign at the numerator, the up sign is to be used if the observer is moving toward the source and the down sign if moving away from the source; in the denominator, the upper sign is used if the source is in motion w.r.t the source towards the observer and the lower sign if moving away.

A simple trick to remember the signs is to remind one when or not the observed frequency is becoming to increase or decrease and to use whenever sign is required. For eg, when an observer is moving away from a source, the wave are going to move across it at the slow rate rather than if it was still, which signifies that the observers frequency is decreasing.

And also it can be for when the source is in motion w.r.t an observer, it will go to “smoosh” the wave together as it emit it, which means to say that the increase in the observed frequency. This will be covered by making the denominator in eq (3) smaller, which do requires using it again.

Source moving with V source < V sound:

In picture shows sound source has radiated sound wave at the const. frequency in the same medium. However, the sound source is turning to the right with a speed Vs = 0.7 V(In mach). The wave fronts are to be produced with the same frequency. Since the source is moving and the center of the new wave front is now slightly shifted to the right. As a result, the wave fronts start bunching on the right side (in front of) and spread further on the left side of source. An observer in the front of the sourceis made to hear it at higher frequency f ´ > f0, and then the observer back to the source will hear a lower frequency f ´ < f0.

Source moving with V source = V sound:

Here the source is moving with the speed of sound in the medium (Vs = V, Mach 1). The wave fronts in front of the source are all bunched up to the same point. An observer in front of the source will feel nothing until the source arrives to him. The front will be quite intense, due to all the wave fronts add together.The figure at right shows a bullet travelling at Mach 1.01. You can see the shock wave front just ahead of the bullet.

Source moving with V source > V sound:

The sound source has been broken through the sound speed barrier, and is traveling at the greater speed then the speed of sound. Here the source is moving faster than that of the sound waves it creates are really leading the advancing wave fronts. It is this intense pressure front on the Mach cone that causes the shock wave known as a sonic boom as a supersonic aircraft passes overhead. The shock wave advances at the speed of sound v, since it has been built up from all of the combined wave fronts, the sound heard to the observer will be of the quite intense.

Application of Doppler Effect:

Sirens: – “The reason why the siren slides or blow, is because it doesn’t hit you.”

It can be says as, if the siren is approaching to the observer directly, the pitch of the sound would remain constant (we have, vs, r is the radial component) till the source hit the observer, and then jump to the lower pitch. Because of the vehicle passes from the observer, the radial velocity never remains constant, but instead to vary as a function of the angle between observer line of sight and the siren’s velocity:

Vr = Vscos θ

Where vs is the velocity of the source w.r.t. the medium, and the angle θ is the angle between the object’s forward velocity and the line of sight from the object to the observer.

Radar:-In the radars Doppler Effect is widely used in some of the radar, to measure the velocity of the object. A sound with required wavelength, intensity is fired to a moving target as it approaches from the radar source. Each subsequent radar wave has to travel farther to reach the object, before being redetected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. Calculations from the Doppler Effect accurately determine the observer’s velocity.

Weather Analysis or prediction: -Doppler radar uses the Doppler Effect for electromagnetic waves to predict the weather.

In Astronomy:-The Doppler shift for light is used to help astronomers discover new planets and binary stars.

Echocardiography: – A medical test uses ultrasound and Doppler techniques to visualize the structure of the heart.

Radio Direction Finding Systems