The Doppler Effect is a very interesting phenomenon that describes the change in the frequency of waves resulting from the relative motion of the source and observer. More commonly applied to sound waves, it also pertains to light and more wave types. It was named after an Austrian physicist by the name of Christian Doppler. It explains why people seem to hear changes in pitch when a moving source of sound would say the passing ambulance seems to change in pitch as it approaches and then recedes.

Formula 

Where,

• f′ = observed frequency,

• f  = emitted frequency (the frequency of the source),

• v  = speed of sound in the medium (approximately 343 m/s in air at 20°C),

• Vo =​ speed of the observer (positive if moving towards the source, negative if moving away)

• Vs​ = speed of the source (positive if moving away from the observer, negative if moving towards).  

Solved Problems

Problem: A Submarine travels through water at 8.00 m/s, and it emits a sonar wave at a frequency of 1400 Hz. The speed of sound in the water is 530 m/s. Second Submarine travels at 6.00 m/s directly towards the first submarine.

(A) What is the frequency detected by an observer riding on the second submarine as the first submarine approaches it?

(B) The submarine barely misses each other and pass. What frequency is detected by an observer riding on the second submarine as the subs recede from it?

(C) When both the submarines are approaching each other, then some of the sounds from the first submarine reflects from the second submarine and returns to it. If the sound were detected by a first submarine, then what is its frequency?

Solution:

Given: Frequency f = 1400 Hz,

Velocity of first submarine, Vs = 8 m/s,

Velocity of second submarine, Vo = 6 m/s.

Speed of sound in water V = 530 m/s

(A) The Apparent frequency is obtained as follows,

f ' = 1437.54 Hz.

(B) Calculate the Doppler-shifted frequency heard by observer in second submarine,

f' = 1363.56 Hz.

(C)Apparent frequency of 1436.5 Hz obtained in part (A) is emitted from a moving source (sub B) and received by a moving observer

f" = 1476 Hz

 

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