Doppler Effect: Overview, Questions, Preparation

As a general rule, the frequency of a wave goes up when the source is approaching us and goes down when the source travels away from us. This motion-related frequency change is called the Doppler Effect. Doppler effect or Doppler shift describes the changes in the frequency of any sound or electromagnetic wave produced by a moving source concerning an observer. It is a wave phenomenon first proposed by Johann Christian Doppler in 1842.

The changes in frequency are analysed under three conditions.

Let us consider a source S moving with a velocity vₛ and an observer O who is stationary and medium at rest. Let the speed of wave of angular frequency ω and period T₀, both measured by an observer at rest for medium v. 

Let’s assume the observer has a detector that counts a wave crest when it reaches it.

At the time, t=0, the source at point S₁ located at a distance L from the observer emits a crest. This reaches the observer at time t₁= L/v.

At time t= T₀, the source has moved a distance vₛT₀ at point S₂. Distance from the observer is L+ vₛT₀ and reaches the observer at time t₂.

After an observer detects ‘n’ crests, the period of the wave is given by

The observer measures high frequency when the source approaches him, and it measures lower frequency when the source moves away from him.

Doppler shift when the observer is moving with velocity and source at rest. The frequency observed is,

If v₀/v is small, the Doppler shift is the same whether the source or observer is moving.

This is the general expression of the Doppler shift when both the source and observer is moving. The frequency v observed by the observer is given by

Doppler Effect for Class 11

The topic falls under the category of minimum weightage (less than 5 marks). Short answers and problem-based questions are more from this topic.

1. A train moving at 40 m/s on a day when the speed of sound is 350m/z has a horn 170Hz. What is the frequency observed by a stationary person as the train approaches and passes by?

2. What is the frequency when source and observer are moving at an angle?

3. If the observer speed is 60 m/s and source speed  is 40 m/s. What is the frequency observed if the observer is moving towards a stationary source if the speed of the sound is 340 m/s and frequency of sound is 1000Hz?

Image courtesy: NCERT