Doppler Effect
The Doppler effect is a wave phenomenon that is easily detected in sound waves. For example, if you are driving on a road and a car passes you. You can easily detect the change in the pitch of the sound. This apparent change in the frequency of sound was predicted by Doppler in the year 1845. Doppler stated that a change in the frequency will occur if a source of sound wave or source of the light wave moves. This variation in the frequency with the motion is known as the Doppler effect.
The phenomenon of the Doppler effect was first applied to the change in the colour of the stars as they approach or recede along the line of sight. The Doppler effect is used in the measurement of the speed of cars, planes, thunderstorms etc.
The apparent change in the frequency due to the relative motion between the source and the observer is known as the Doppler effect.
Doppler Effect in Sound
Let us consider a sound wave of frequency f emitted from a source of sound propagating through the medium with a speed v. The wave is propagating along the positive x-direction. The speed of the wind blowing in the positive x-direction is vW and the listener also moves with a velocity vL in the positive x-direction.
Case 1. If the source and the listener are at rest and λ is the wavelength of the sound waves, then
v = fλ
Here, f is the true frequency and λ is the true wavelength
Case 2. If the source of sound travels a distance of vS in one second. Then the sound waves will travel a distance of V in this time. Since the wind also blows in the same direction the waves will travel an additional distance of vw.The apparent frequency as heard by the moving listener is
f’= [ (v + vw-vL) / (v + vw – vs)] f
Doppler Effect in Light
Light waves also exhibit the Doppler effect. In examining the Doppler effect in the light waves, we do not distinguish the motion of the observer and the motion of the light source. When the source of light like the Sun, Star etc approaches and recedes from the observer, the frequency of the light waves appears to change.
When there is a decrease in the separation between the source and the observer the frequency of the light appears to increase or in other words, the wavelength decreases. Then, the spectral lines in the electromagnetic spectrum get shifted to the violet. This is called violet shift.
When there is an increase in the separation between the source and the observer, then the frequency of light appears to decrease or the wavelength appears to increase. In this case, the spectral lines in the electromagnetic spectrum get shifted to red. This is called redshift.
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