# Doppler Effect

## Doppler Effect

As a rule, the speed of sound in daily life is much higher than our movement.

But with faster movement, such as fast moving objects – cars, trains, the relative speed between the object and the listener will affect the frequency of the sound we perceive.

Thus, if a sound source is moving relative to the recipient or conversely the frequency of the perceived sound is changed in proportion to the speed of movement.

Trains, airplanes – there is a change in the pitch of the perceived sound. As the subject moves against us or vice versa – the pitch increases and decreases respectively.

An interesting analogy can be made by moving the swan on the surface of a lake – the moving object is catching up the waves it creates, thus in the front we have thickening of the oscillation of the water surface and the back – dilution:

Another analogy could be made with two participants in the ball game where one player throws the ball to the other with a uniform velocity. If he starts to approach the second participant, keeping the speed of the throwing, the second player will have to catch more balls per unit of time. If the first is moving away – they will become less per unit of time.

Although the movement in nature has a relative character, ie no matter which object moves against which, the  Doppler effect is expressed differently for subject movement to the recipient and the recipient to the object. This is due to the fact that in this case the relativity applies to cases where there is no conducting medium between the source and the listener. When there is such medium, it matters against which participant in the process moves, and which – not.

For this reason the Doppler effect is described by different formula depending on who from the the participants in this process is moving in the moment.

For example in a moving sound source in direction towards the recipient we have the relationship:

where:

C  is the velocity of waves in the medium;

is the velocity of the observer relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);

is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction),

f is the frequency we perceive, and

f0 – the frequency of the initial transmission of sound.

Despite the apparent complexity of these specifications, in most cases one of following values  –

and

can be removed, since only one of the participants in the process is moving. The formula in it’s full size is applicable only under mutually movement of the sound source and the recipient.

For example, if we have an object, moving towards us with 10 m / s, which is  emitting a frequency of 1000 Hz, then we can calculate:

f = 1000 x 340/(340-10),

since 340 is the speed of sound – 340 m / s, the initial frequency – 1000Hz, and the speed of the object – 10 meters / sec.

Thus the sound we shall hear will be 1030.3 Hz.

In this example, the value v0 is not involved, as we do not move towards the object.

At speeds of the sources, which are close to the speed of the sound, we have an exponential increase in the frequency because the source starts catching up the already emitted sound waves, while emitting during this time new ones:

Thus is obtained a superimposition of the sound waves, thereby there is created a resultant acoustic front from the interference of the overlapping fronts.

When passing the speed of sound,  that front tears, creating in this moment a specific sonic explosion, typical for the crossing of the sound barrier.
Practically when moving with greater speed from the speed of sound, the sound waves begin to lag behind the sound source. Lord Rayleigh has established an interesting theoretical formulation, that if we have a sound source moving at a speed two times the speed of sound, the music emanating from this source would be heard from a stationary observer with the same frequency, but backwards.

Doppler effect other than its attractive development by glissando sound in the passage of a fast object beep is also useful in other areas. Since it allows for to a specified base speed of flow of the waves in a medium to be measured the deviation and thereby the velocity of the wave to be calculated, it can be applied in the field of sound, but  is not limited to it. Since the spectrum of a body emitting electromagnetic radiation (eg light) is determined by the frequency, in astronomy there can be made observations about the speed and direction to our movement of these objects, which are based on the deviations caused by the Doppler effect – so called red and blue shift in the spectrum of the waves.

The spectrum of the bodies emitting electro-magnetic oscillation is not uniform. It has absorption lines due to  the stepwise transition of the electrons of the atoms from one energy state to another.

When there is a Doppler shift, these absorption lines are moving along the spectrum to the red area, if the object is moving away, and to blue if approaching. This enables us to explore the movement of distant objects – stars and galaxies.

When we talk about glissando in the sound caused by the movement of the object to us or our relation to it (will later clarify what is the difference between the two), we must consider that glissando occur only in a situation where we have angular motion and not exactly opposite. In such a movement the frequency of the sound decreases because actually we have at the same time reducing the speed of approaching of the object relative to us, and consequently increase the speed of moving away. This leads to a glissando effect.

If we stand on the platform and the train is coming almost straight at us, and then moves away in the same way, we have a jump-like change of height, not a gliss effect.

This change is currently happening on the moment of alignment of the train against us, at which time the relative speed becomes reversed.

### now the exercise:

#### And if it is moving backwards with the same speed?

Here is the graph of the tones in the musical scale:

### Written byHristo

Filed under: Sound theory