Unit 2: Doppler Effect Equation

The frequency emitted by the source (fs) is constant, only the frequency detected by the listener changes provided there is a relative motion between the source of sound waves and the listener. We can use the following equation to calculate the frequency heard by the observer (listerer):

f L = frequency heard by observer (listener), measured in Hertz (Hz)
f S = frequency of source (Hz), measured in Hertz
v = speed of sound in medium, measured in meters per second ( m∙s-1)
vL = speed of observer (listener), measured in meters per second (m∙s-1)
vS = speed of source, measured in meters per second (m∙s-1)
Doppler expressions to use after writing the Doppler effect formula

Using the plus (+) or minus (–) signs depends on the relative motions of the source and observer.

Examples
Both the SOURCE and LISTENER are STATIONARY
The siren of a stationary ambulance emits waves at a frequency of 800 Hz. Determine the frequency of the sound heard by a stationary observer if the speed of sound in air is
340 m∙s-1.
Solution
f L = ?
f S = 800 Hz
v = 340 m∙s-1
v L = 0 m∙s-1
v S = 0 m∙s-1

When the SOURCE and the LISTENER are STATIONARY, then the frequency observed by the LISTENER is the SAME as the frequency of the SOURCE. There is NO Doppler Effect.

THE SOURCE is MOVING TOWARDS a STATIONARY LISTENER
An ambulance is moving towards a stationary listener with a velocity of 30 m∙s-1. The frequency emitted by the ambulance is 600 Hz. Calculate the frequency that the listener will detect, if the speed of sound in air is 340 m∙s-1.
Solution
f L = ?
f S = 600 Hz
v = 340 m∙s-1
v L = 0 m∙s-1
v S = 30 m∙s-1

When the source is moving TOWARDS a stationary listener, then the frequency observed by the listener is HIGHER THAN the frequency of the source.

The SOURCE is MOVING AWAY from a STATIONARY LISTENER:
An ambulance is moving away from a stationary listener with a velocity of 25 m∙s-1. The frequency emitted by the ambulance is 450 Hz. Calculate the frequency that the listener will detect, if the speed of sound in air is 340 m∙s-1.
Solution
f L = ?
f S = 450 Hz
v = 340 m∙s-1
v L = 0 m∙s-1
v S = 25 m∙s-1

When the source is moving AWAY from a stationary listener, then the frequency observed by the listener is LESS THAN the frequency of the source.