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.

Login

Accessing this course requires a login. Please enter your credentials below!