Some Important Aspects of Doppler Effect

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• When a source moves towards a stationary observer the apparent frequency, according to equation

• When the observer moves towards a stationary source, the apparent frequency, according to equation

In both the cases, the apparent frequency is greater than the actual frequency. For comparing the apparent frequencies, let us assume that a = b, in magnitude. Let the apparent frequencies in the two cases be denoted by f₁ and f₂. Then

and

Since the denominator in the RHS of the above equation is less than 1, f₁ > f₂. Thus, the increase in the apparent frequency is greater when the source approaches a stationary observer than, when the observer approaches a stationary source. In other words, Doppler effect in sound is 'asymmetric'. This asymmetry is not observed in Doppler effect in case of light. This is due to the fact that the velocity of light is very high when compared to the velocity of the source or the observer.

• If the observer moves away from the source with a speed greater than the speed of sound, then the wave can never 'catch up' with the observer and the formula should not be applied. Another problem arises when the source moves with a velocity exceeding the velocity of sound. Equation (1-39) then, predicts a negative frequency. Since this does not make any physical sense, a different interpretation has to be given. Consider the source moving from the point A to B in a time t with a velocity greater than v, the velocity of sound. By the time the source reaches B, the sound wave from A will have covered a distance vt. The wavefront is shown by the largest circle in the figure. These wavefronts become smaller and smaller in size until the zero radius is reached at B. The envelope of these wavefronts is a cone (called the Mach Cone) whose surface makes an angle q with the direction of motion of the source. From the figure

The ratioi.e., the ratio of the velocity of a body to the velocity of sound is called the Mach number.

The conical envelope represents a very narrow region of high pressure called the 'shockwave'. Some examples of the formation of the shockwaves are when

(i) a supersonic aircraft flies across the sky

(ii) a bullet is shot from a gun.

A shockwave is a highly concentrated sound wave and is therefore, a pressure wave. It is this wave of increased pressure that produces a sound like a thunderclap or an explosion.

• The Doppler effect can be observed in all kinds of waves so long as the speed of the source is small when compared to the speed of the wave. The observed shift towards the red (lower frequencies) in the spectra of some stars indicate that the stars are moving away from the observers on the Earth and gives support to the 'expanding universe' concept.