Effect of Motion of Medium on Apparent Frequency

What is the Doppler effect?

When an object is moving with respect to the observer, then a phenomenon is observed, which is known as the Doppler effect. A typical example of the Doppler effect is when an ambulance comes closer to you from the back, and the siren is on. You will observe an increase in the sound when the van comes closer to you. However, once the van moves away from you, the sound decreases. In this case, you can judge the distance of the ambulance van only by hearing the sound of the siren. 

The various factors that contribute to the Doppler effect are:

• The motion of the observer
• The motion of the source
• The motion of the medium

Formula of the Doppler effect

Doppler effect is generally expressed as follows:

Where,

c is the speed of propagation of waves in the medium

vr is the speed of the receiver with respect to the medium; +c if the receiver is moving toward the direction of the source and -c if the receiver is moving opposite to the source.

vc is the speed of the source with respect to the medium +c if the receiver is moving towards the direction of the source and -c if the receiver is moving opposite to the source.

This equation varies according to the velocity of the observer and the speed of the sound. 

Change in apparent frequency due to moving objects

If the medium is moving, then there will be two cases. We will discuss those two cases in the following section:

1. The medium is moving from source to the observer: Let me explain this concept with the help of an example. A wind is blowing from the source to the observer with a speed of Vw. The direction of the velocity of the wind is the same as the direction of the velocity of the sound. In this case, the velocity of the sound V will become V + Vw. This new V will be substituted in the formula of the Doppler effect. The formula mentioned above of the Dopplers effect is derived considering the medium is at rest. 

1. The medium is moving from observer to source: In this situation, the wind is blowing from the observer to the source with the speed of Vw. The direction of the velocity of the wind will be opposite to the direction of the velocity of the medium. Then the velocity of the sound V will be V – Vw. You have to substitute this new velocity in the formula to retrieve the answer. 

Limitations of the Doppler effect

The Doppler effect is not without drawbacks. The demerits of the Doppler effect is that it comes into play or can be observed only:

• When the velocity of the sound is higher than the velocity of the sound source and the velocity of the observer. 

• When the motion of the observer as well as the source is in the direction of the same straight line.

Applications of the Doppler effect

The Doppler effect finds its applications in vast fields like:

• Astronomy: The Doppler effect helps to measure the speed of the motion of the stars towards the earth. 
• Radars: Radars work on the principle of the Doppler effect. It is an effective technique to find the speed of the detected objects with this effect. 
• Sirens: The sirens of many vehicles reflect this effect. You can use your hearing sense to detect whether the vehicle is approaching you or moving away from you. The principle hidden behind this phenomenon is the Doppler effect. 
• Audio: To detect the fluctuating sounds of frequencies, the Doppler effect is of great help. 

Conclusion 

This article covers almost everything on this important topic of the effect of motion of medium on apparent frequency. The main principle working behind these phenomena is the Doppler effect. 

You will learn about the Doppler effect, followed by cases of the Doppler effect. The formula of the Doppler effect varies according to different scenarios, e.g. if the source is approaching the observer or the observer is approaching the source and with what velocity and speed. In the end, you will also learn about the limitations and applications of the Doppler effect.