Chapter 14 The Doppler Effect
Norjuliyati Binti Hamzah norjuliyati@uitm.edu.my
At the end of the lesson, the students should be able to: ď ą Explain the Doppler effect and its applications. ď ą Apply the Doppler general equation.
The Doppler Effect
A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves. Assumptions: The air is stationary All speed measurements are made relative to the stationary medium
The Doppler Effect Case 1: (Moving Observer) Observer Toward Source An observer is moving toward a stationary source Due to his movement, the observer detects an additional number of wave fronts The frequency heard is increased When moving toward the stationary source, the observed frequency is
v vo fo fs v
The Doppler Effect Case 1: (Moving Observer) Observer Away from Source An observer is moving away from a stationary source The observer detects fewer wave fronts per second The frequency appears lower When moving away the stationary source, the observed frequency is
v vo fo fs v
The Doppler Effect Doppler Effect for Moving Observer
v vo fo fs v vo = observer speed SI unit: 1/s = s = Hz v = wave speed Substitute (+ v0) for v0 in the equation when the observer moves toward the source. -1
Substitute (– v0) for v0 in the equation when the observer moves away from the source.
The Doppler Effect Case 2: (Moving Source) Source Toward Observer As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases When source is moving toward the observer, the observed frequency is
v f o f s v vs
The Doppler Effect Case 2: (Moving Source) Source Away from Observer As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower When source is moving away from the observer, the observed frequency is
v f o f s v vs
The Doppler Effect Doppler Effect for Moving Source
v f o f s v vs
vs = source speed SI unit: 1/s = s = Hz v = wave speed Substitute (+ vs) for vs in the equation when the source moves toward from the observer. -1
Substitute (– vs) for vs in the equation when the source moves away from the observer.
The Doppler Effect Combining results gives us the case where both observer and source are moving: Doppler Effect for Moving Source and Observer
v vo f o f s v vs SI unit: 1/s = s-1 = Hz The Doppler Effect does not depend on distance As you get closer, the intensity will increase The apparent frequency will not change
Example A train moving at a speed of 40.0 m/s sound its whistle, which has a frequency of 5.00 Ă— 102 Hz. Determine the frequency heard by stationary observer as the train approaches the observer. The ambient temperature is 24.0oC.
Solution ď ą Determine the frequency heard by stationary observer as the train approaches the observer.
Example An ambulance travels down a highway at a speed of 75.0 mi/h, its siren emitting sound at a frequency of 4.00 Ă— 102 Hz. What frequency is heard by a passenger in a car travelling at 55.0 mi/h in the opposite direction as the car and ambulance (a) approach each other and (b) pass and move away from each other? Take the speed of sound in air to be v = 345 m/s.
Solution a) approach each other
b) pass and move away from each other
Summary of Chapter Doppler Effect ď ą Doppler effect: change in frequency due to relative motion of sound source and receiver ď ą General case (both source and receiver moving):