# Doppler Shift

Doppler effect or Doppler shift refers to a phenomenon that one can observe whenever the movement of the source of waves takes place with respect to an observer. Furthermore, a common physical demonstration of the Doppler shift can be an ambulance crossing something with its siren blaring. Also, the Doppler shift is an important phenomenon that plays an important role in a variety of different scientific disciplines.

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## Introduction to Doppler Shift

The Doppler effect or the Doppler shift describes the changes in the frequency of any kind of light or sound waves whose production takes place by a moving source with respect to an observer. Furthermore, Doppler effect in physics refers to the increase or decrease in the frequency of sound, light, or other waves when the source and observer are moving towards each other or away from each other. Moreover, the naming of this concept is after the Austrian physicist Christian Doppler, who is known for describing the phenomenon in 1842.

A common Doppler effect example is the change of pitch that someone hears when the approaching of a vehicle sounding a horn takes place and recedes from an observer. In comparison to the emitted frequency, the received frequency tends to be higher during the approach, identical when the passing by happens and lower when the recession takes place.

Doppler Shift

### Formulas of Doppler Shift

Doppler effect refers to the apparent change in the frequency of waves due to the relative motion between the source of the sound and the observer. Furthermore, one can deduce the apparent frequency in Doppler effect by making use of the equation below:

$$f{}’= \frac{\left ( v\pm v_{0} \right )}{\left ( v\pm v_{s} \right )}f$$

Where,

$$f{}’$$ = observed frequency

f = actual frequency

v = velocity of sound waves

v0 = velocity of observer

Also, vs = velocity of the source

While there is only one Doppler effect equation, change takes place in the above equation changes due to different situations depending on the velocities of the observer or the sound’s source. Below is the use of the Doppler effect equation in different situations.

(a) When the source moves towards the observer at rest

In this case, the velocity of the observer is zero, so v turns out ot be zero. Substituting this into the Doppler effect equation above, one would derive the equation of the Doppler effect when the movement of a source takes place towards an observer at rest as:

$$f{}’= \frac{v}{\left ( v-v_{s} \right )}f$$

Where,

$$f{}’$$ = observed frequency

f = actual frequency

v = velocity of sound waves

Also, vs = velocity of the source

(b) When the movement of the source takes place away from the observer at rest

Since the velocity of the observer is zero, elimination of v0 is possible from the equation. But this time, the movement of the source takes place away from the observer, so its negative velocity is an indication of  the direction. Hence, the equation now becomes:

$$f{}’= \frac{v}{\left ( v-\left ( -v_{s} \right ) \right )}f$$

Where,

$$f{}’$$ = observed frequency

f = actual frequency

v = velocity of sound waves

Also, vs = velocity of the source

$$f{}’= \frac{343m/s}{\left ( 343m/s)+25m/s \right )}1.000Hz = 932Hz$$

(c) When the observer is moving towards a stationary source

This is another important Doppler shift formula. In this case, vs turns out to be zero, hence one would get the following equation:

$$f{}’= \frac{\left ( v+v_{0} \right )}{v}f$$

Where,

$$f{}’$$ = observed frequency

f = actual frequency

v = velocity of sound waves

Also, v0 = velocity of observer

(d) When the observer is moving away from a stationary source

Since the movement of the observer is away, the velocity of the observer turns out to be negative. Therefore, instead of adding v0, subtraction must take place as vo is negative.

$$f{}’= \frac{\left ( v-v_{0} \right )}{v}f$$

Where,

$$f{}’$$ = observed frequency

f = actual frequency

v = velocity of sound waves

Also, v0 = velocity of observer

## FAQs For Doppler Shift

Question 1: What is meant by the Doppler shift?

Answer 1: The Doppler Doppler shift describes the changes that take place in the frequency of any kind of wave whose production takes place due to a moving source with relation to an observer.

Question 2: Explain the working of the Doppler shift?

Answer 2: Doppler effect simply refers to the increase (or decrease) in the frequency of sound, light, or other waves as the source and observer are moving towards each other or away from each other. Furthermore, there is a compression of waves emitted by a source travelling towards an observer. In contrast, there is stretching out of waves emitted by a source travelling away from an observer.

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