Moving Source

The Doppler effect is the apparent change in frequency of a wave when the observer and the source of the wave move relative to each other.

Learning Objective

Identify parameters required to calculate the perceived frequency of the sound source moving towards an observer

Key Points

When the object in motion moves towards the other, the frequency is increased because the time between successive sound waves is shortened (therefore the pitch is higher).
When the object in motion moves away from the other, the frequency is decreased because the time between successive sound waves is lengthened (therefore the pitch is lowered).
Unless the objects are in each other's direct path, you need to account for their angle relative to each other. The following equation must be substituted for the 'movers' velocity. The angle used must be the angle from the line of sight of the observer to the sound source.

Term

The Doppler Effect
Apparent change in frequency of a wave when the observer and the source of the wave move relative to each other.

Example

Suppose a train that has a 150-Hz horn is moving at 35.0 m/s in still air on a day when the speed of sound is 340 m/s. What is the observed frequency of the horn as the train approaches the observer? Lets start by making a list of the terms we have and what we need: c - 340 m/sf0 - 150 Hzvs - 35 m/svr - 0 m/s$\theta$ - For this example, lets assume the observer is so close to the train tracks that the angle is negligible. $f=\frac{c}{c+v{s}}*f_0\\ f=\frac{340{\frac{m}{s}}}{340{\frac{m}{s}}+35\frac{m}{s}}*150Hz\\ f=0.907*150Hz\\ f=136Hz$

Full Text

The Doppler Effect—When the Sound Source is in Motion

When the sound source moves toward an observer, each successive wave is emitted closer to the observer than the previous wave and takes just a little less time to reach the observer than the previous one. Since the time between waves is reduced, the frequency is increased. Similarly, if the sound source is moving away from the observer, the frequency (and therefore pitch) is decreased. While the frequency will change whether the observer or sound source is moving, the effect is more easily demonstrated by the sound source. This Doppler Effect is illustrated in .

The Doppler Effect

The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed υs = 0.7 c (Mach 0.7). The wave-fronts are produced with the same frequency as before. However, since the source is moving, the centre of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source.

Unless the observer is moving directly towards the sound source, this angle must be considered when calculating the newly perceived frequency. Before attempting this calculation, we must know:

The original sound wave frequency, f₀
The velocity of the observer, v_r
The speed of sound in the air, or medium, c
The angle of the line of sight from the observer to the sound source, $\theta$

Although the sound waves are being emitted from the sound source at a uniform frequency, the observer is perceiving them differently. The equation for the perceived wave frequency is as follows:$f=\frac{c}{c{\pm}v_{s,new}}*f_0$And the equation for v_s, is:$v_{s,new}=v_s*cos\theta$

If the sound source is moving towards the observer, a plus sign is used in front of the sound source's velocity. If the sound source is moving away from the observer, then a negative sign is used in front of the sound source's velocity.

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