1.2 Doppler effect
a. define Doppler effect.
b. understand that whenever there is a relative motion between the source of wave and the observer there is a change in the observed frequency.
c. use the expression f0 = to solve problems for the observed frequency for various cases: 1. moving source of wave 2. moving observer 3. both moving source of wave and moving observer
d. appreciate that Doppler effect is observed with all waves, including sound and light. (Applications of Doppler effect need not to be discussed in light)
Doppler Effect is the change in frequency of a wave when there is relative motion between the source and observer. It is the increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other.
Example: Two people A and B, are standing on the road, as shown below in the picture
Person A hears the sound of the revving engine with a greater magnitude than person B. Person B, standing behind the car, receives fewer waves per second (because they’re spread out), resulting in a low-pitched sound. But, person A who is in front of the car, receives more of those soundwave ripples per second. As a result, the frequency of the waves is higher, which means the sound has a higher pitch.
Video link : https://youtu.be/CbyA8S2kTzk
Doppler effect is the apparent change in the frequency of waves due to the relative motion between the source of the sound and the observer. We can deduce the apparent frequency in the Doppler effect using the following equation
While there is only one Doppler effect equation, the above equation changes in different situations depending on the velocities of the observer or the source of the sound. Let us see below how we can use the equation of the Doppler effect in different situations.
1. Source Moving Towards the Observer at Rest
In this case, the observer’s velocity is zero, so vo is equal to zero. Substituting this into the Doppler effect equation above, we get the equation of the Doppler effect when a source is moving towards an observer at rest as:
2. Source Moving Away from the Observer at Rest
Since the velocity of the observer is zero, we can eliminate vo from the equation. But this time, the source moves away from the observer, so its velocity is negative to indicate the direction. Hence, the equation now becomes as follows:
3. Observer Moving Towards a Stationary Source
In this case, vs will equal to zero, hence we get the following equation:
4. Observer Moving Away from a Stationary Source
Since the observer is moving away, the velocity of the observer becomes negative. So, instead of adding vo, we now subtract, since vo is negative.
Doppler Effect Solved Problems
1. Two trains A and B are moving towards each other with a speed of 432 km/h. If the frequency of the whistle emitted by A is 800 Hz, then what is the apparent frequency of the whistle heard by the passenger sitting in train B. (The velocity of sound in air is 360 m/s).
2. A bike rider approaching a vertical wall observes that the frequency of his bike horn changes from 440 Hz to 480 Hz when it gets reflected from the wall. Find the speed of the bike if the speed of sound is 330 m/s.
Uses of Doppler Effect
Many mistake the Doppler effect to be applicable only for sound waves. It works with all types of waves including light. Below, we have listed a few applications of the Doppler effect
A few daily life examples of Doppler effect are: a) When you stand beside a police radar. b) The Doppler effect is used by meteorologists to track storms. c) Doctors use the Doppler Effect in hospitals to diagnose heart problems. d) Traffic police make use of doppler effect a radar gun to check the speed of the oncoming vehicle
Doppler Effect Limitations
- Doppler Effect is applicable only when the velocities of the source of the sound and the observer are much less than the velocity of sound.
- The motion of both source and the observer should be along the same straight line.
Doppler Effect In Light
Doppler effect of light can be described as the apparent change in the frequency of the light observed by the observer due to relative motion between the source of light and the observer. For sound waves, however, the equations for the Doppler shift differ markedly depending on whether it is the source, the observer, or the air, which is moving. Light requires no medium, and the Doppler shift for light travelling in a vacuum depends only on the relative speed of the observer and source.