The Doppler Effect

Imagine you are standing on the sidewalk with your eyes closed. Then you hear the sound of an ambulance's siren in the distance but you do not know how far away from you it is. Somehow, you are still able to intuitively tell when the ambulance has passed you even though the ambulance's siren is transmitting at the same frequency all the time.

Our ability to determine when the ambulance has passed is due to the Doppler Effect

If there is relative motion between the source of sound and the receiver of sound, the frequency at the receiver is different from the frequency that is transmitted.

If 2 objects are moving towards each other the received frequency is higher and if they are moving apart, it is lower

high frequency low frequency

A stationary source emits spherical waves that travel outward at the same velocity in all directions. A receiver at any point around the source will detect the same frequency.

If the source is moving to the right, the wave fronts to the right of the source are closer and are more spread out to the left. The waves are still travelling at the same speed so a receiver on the right will detect more waves per second than on the right.

3 possible scenarios:

moving source and receiver

stationary receiver, moving source

stationary source, moving receiver

Notice the signs in the numerator and denominator are different.

• If the receiver is moving towards the source we observe an increased frequency and use the stop sign in the numerator.

• If the source is moving toward the receiver we also observe an increased frequency and use the top sign in the equation.

fs=frequency at source

fr=frequency at receiver

vs=velocity of source

vr=velocity of receiver

v=speed of sound =343m/s

Another way to think about the Doppler effect:

Recall that the speed of sound in air at a given temperature is constant. The wavelength on the right of the source is clearly shorter.

Since f=v/λ, a shorter wavelength requires a higher frequency to maintain the same velocity.

Sample Question

A driver is travelling at a speed of 85km/h on a highway. An ambulance is travelling in the opposite direction on the same highway at a speed of 120km/h with its siren producing sound at 2500Hz.

a)What frequency does the driver observe as the ambulance approaches him?

b)What frequency does the driver observe as the ambulance passes him?

c)If the car decides to pull over when it hears the ambulance what frequency does it observe as the ambulance approaches and passes him?

SolutionBegin by converting the speeds from km/h to m/s

85km/h * 1000m/km * 1h/3600s = 23.6m/s

120km/h * 1000m/km * 1h/3600s = 33.3m/s

a) The 2 cars are approaching one another, use the formula

fr=(v+vr)/(v-vs)*fs

=(343+23.6m/s)/(343-33.3m/s)*2500Hz

=2959Hz

b) The 2 cars moving away from one another, use the formula

fr=(v-vr)/(v+vs)*fs

=(343-23.6m/s)/(343+33.3m/s)*2500Hz

=2122Hz

c) As the ambulance approaches and car is stationary

fr=(v)/(v-vs)*fs

=343/(343-33.3m/s)*2500Hz= 2769Hz

As the ambulance passes and car is stationary

fr=(v)/(v+vs)*fs

=343/(343+33.3m/s)*2500Hz= 2279Hz