The Doppler EffectThe Concept Explained!

● The phenomena that the wave

frequency changes when the

distance between a source of

sound and a receiver of sound:

o If the objects are coming

closer to one another, the

frequency increases

o If they are moving farther

away from each other, the

frequency decreases.

Introduction

http://www.redorbit.com/media/upl

oads/2004/10/6_2794e0fcae75d8

49e10a80c3137aa8bc2.jpg

There are three cases related to the

doppler effect that can be modeled by a

simple equation.

● stationary source + moving receiver

● stationary receiver + moving source

● moving source + moving receiver

Cases of Doppler Effect

The equation used to model these 3 cases:

Equation

Vr = velocity of the

receiver

Vs = the velocity

of the source

fr = the frequency

of the receiver

fs = the frequency

of the source

Note the ± and ∓ in the numerator and denominator of the equation.

● Use the top sign of the numerator if the receiver is moving towards

the source. There is an observed increase in frequency

● Use the top sign of the denominator if the source is moving towards

the receiver. There is also an increase in frequency observed.

For the next couple of slides we will

be looking at how the doppler effect

occurs in the sounds of an emergency

vehicle siren.

Emergency Vehicle Siren and You

Let’s Pretend that the Source

was Stationary

● emits spherical waves with

the same speed in all

directions

● Receiver at any point will

detect the same frequency

because they are equally

spaced apart http://cfcpwork.uchicago.edu/kic

p-

projects/nsta/2007/sherman/dop

pler_files/image004.png

1) Moving Source + Stationary Receivero Imagine that an emergency vehicle is

approaching you from the left and continues

to move right.

Special Cases when vr= 0 or vs = 0

http://mail.colonial.net/~hkaiter/aa_newest_images/doppler.effect.diagram.jpg

● Distances between wave fronts at the

right side of the source are closer

together than the wave fronts at the left

of the source

● Waves are still travelling at the same

speed.

● Smaller distance between the wave

fronts on the right, a receiver would

detect more waves per second = higher

frequency

http://cfcpwork.uchicago.edu/kicp-

projects/nsta/2007/sherman/doppler_fi

les/image004.png

2) Moving Receiver + Stationary Source

● receiver detects a reduction in the wave

speed

Special Cases when vr= 0 or vs = 0

First let’s think of it in this way:

Let’s pretend that the receiver was moving

towards the stationary source!

Let’s look at this from a different

approach:

● If the receiver was one crest away from

away from the source, the distance

would be one wavelength away from the

source

● the speed from the perspective of the

receiver would be v+vr since it would

experience more waves per second

● The numerator would have a minus sign

when we plus this into the equation

In the end we get:

Stationary SourceStationary Receiver

Upper sign = motion towards

Lower sign = motion away