Question

Whai is Doppler effect and its application

Answer 1

What causes the Doppler Effect?

The Doppler Effect is caused when the source of a waveform—such as sound or light—sends out waves at a regular rate or frequency, but there is a constant relative motion between the source and observer, causing the observed frequency to change.The Doppler Effect is the change in the observed wavelength or frequency of a waveform, as compared with that emitted from the source, when the source and/or observer are moving with respect to the wave medium.

Examples include hearing the change in pitch of a siren as an ambulance approaches you and observing the change in color—or red-shift—of a star that is moving in a direction away from the Earth.

This effect was named after Austrian scientist Christian Doppler, who discovered the phenomenon for light in 1842. Dutch chemist Buys Ballot verified the Doppler Effect for sound in 1845.

Answer 2

DOPPLER'S EFFECT

Non - Relativistic Treatment

As most readers must have read in physics according to. This phenomenon the pitch sound observed by an observer is different in two cases, firstly when both the source and observer are stationary and secondly when there is relative motion between them. When source and observer are approaching each other, the apparent frequency is increased and when receding, decreased. This phenomenon is called doppler's effect which occurs with all kinds of wave motion, although in case of mechanical waves involving a material medium, its nature is some what different from the case of electromagnetic waves such as light where no medium is involved . In the case of light waves, if spectrum is observed in a spectrometer, a shift in the position of spectral line from the original position is observed with the motion of source.

we first consider the case when the observer is at rest and the source is moving towards it velocity u. let the frequency of the source be f so that the time period

T=1/f

and the wave speed be c in a time time interval T during which one cycle of wave is emitted the wave progresses a at distance cT but in the same period the source wave in the same direction distance u T hence wavelength which is distance between two successive maximum in the wave is cT-uT instead of cT.

Hence the corresponding frequency denoted by f1' its given by

f1'= c/ T(c-u)= cf/c-u

= f/ 1-(c/u)........ (1)

which represents and Apparent increase in the frequency if the source is moving away from the observer we put - u in place of u in equation( 1st) and get the corresponding f1'

in the second case When the source is stationary but the observer is moving with the velocity v from the source the wave is speed relative to the observer is not c but c-v and hence apparent frequency in the case is.

$f \tiny{2} = \frac{c - v}{ \lambda}$

= c-v/c/f

= c-v/c*f

$1 - \frac{v}{c} f \: .......(2)$

f.......(2)

now both observer and source are moving

$\bf{\lambda \tiny{1} = \frac{c}{f \tiny{1}} }$

= $\frac{c - u}{ \lambda}$