BLESSING INTERNATIONAL. SR.

Sec school
Physics art integrated project
On
Creating a visual Doppler effect
Done by
Name : Saipriya.S
Class : XII – “ B “
Roll no : 715
Session: 2024-2025

Aim:
To create a Doppler effect by observing a change in frequency of a sound source as it moves
relative to an observer.
Theory:
The characteristic sound of a motorcycle buzzing by is an example of the Doppler effect.
Specifically, if you are standing on a street corner and observe an ambulance with a siren
sounding passing at a constant speed, you notice two characteristic changes in the sound of
the siren. First, the sound increases in loudness as the ambulance approaches and decreases
in loudness as it moves away, which is expected. But in addition, the high-pitched siren shifts
dramatically to a lower-pitched sound. As the ambulance passes, the frequency of the sound
heard by a stationary observer changes from a constant high frequency to a constant lower
frequency, even though the siren is producing a constant source frequency. The closer the
ambulance brushes by, the more abrupt the shift. Also, the faster the ambulance moves, the
greater the shift. We also hear this characteristic shift in frequency for passing cars, airplanes,
and trains.
The Doppler effect Is an alteration in the observed frequency of a sound due to motion of
either the source or the observer. Although less familiar, this effect is easily noticed for a
stationary source and moving observer. For example, if you ride a train past a stationary
warning horn, you will hear the horn’s frequency shift from high to low as you pass by. The
actual change in frequency due to relative motion of source and observer is called a Doppler
shift. The Doppler effect and Doppler shift are named for the Austrian physicist and
mathematician Christian Johann Doppler (1803–1853), who did experiments with both
moving sources and moving observers. Doppler, for example, had musicians play on a moving
open train car and also play standing next to the train tracks as a train passed by. Their music
was observed both on and off the train, and changes in frequency were measured.
What causes the Doppler shift? Figure illustrates sound waves emitted by stationary and
moving sources in a stationary air mass. Each disturbance spreads out spherically from the
point at which the sound is emitted. If the source is stationary, then all of the spheres
representing the air compressions in the sound wave are centered on the same point, and the
stationary observers on either side hear the same wavelength and frequency as emitted by
the source (case a). If the source is moving, the situation is different. Each compression of the
air moves out in a sphere from the point at which it was emitted, but the point of emission
moves. This moving emission point causes the air compressions to be closer together on one
side and farther apart on the other. Thus, the wavelength is shorter in the direction the
source is moving (on the right in case b), and longer in the opposite direction (on the left in
case b). Finally, if the observers move, as in case ©, the frequency at which they receive the
compressions changes. The observer moving toward the source receives them at a higher
frequency, and the person moving away from the source receives them at a lower frequency.

(a) When the source, observers, and air are stationary, the wavelength and frequency are
the same in all directions and to all observers.
(b) Sounds emitted by a source moving to the right spread out from the points at which they
were emitted. The wavelength is reduced, and consequently, the frequency is increased in
the direction of motion, so that the observer on the right hears a higher-pitched sound.
The opposite is true for the observer on the left, where the wavelength is increased and
the frequency is reduced.
(c) The same effect is produced when the observers move relative to the source. Motion
toward the source increases frequency as the observer on the right passes through more
wave crests than she would if stationary. Motion away from the source decreases
frequency as the observer on the left passes through fewer wave crests than he would if
stationary.
We know that wavelength and frequency are related by
Where v is the fixed speed of sound. The sound moves in a medium and has the same
speed v in that medium whether the source is moving or not. Thus, f multiplied by

Is a constant. Because the observer on the right in case (b) receives a shorter wavelength,
the frequency she receives must be higher. Similarly, the observer on the left receives a
longer wavelength, and hence he hears a lower frequency. The same thing happens in
case (c). A higher frequency is received by the observer moving toward the source, and a
lower frequency is received by an observer moving away from the source. In general,
then, relative motion of source and observer toward one another increases the received
frequency. Relative motion apart decreases frequency. The greater the relative speed, the
greater the effect.

The Doppler effect occurs not only for sound, but for any wave when there is relative
motion between the observer and the source. Doppler shifts occur in the frequency of
sound, light, and water waves, for example. Doppler shifts can be used to determine
velocity, such as when ultrasound is reflected from blood in a medical diagnostic. The
relative velocities of stars and galaxies is determined by the shift in the frequencies of
light received from them and has implied much about the origins of the universe. Modern
physics has been profoundly affected by observations of Doppler shifts.

Derivation of the observed frequency due to Doppler shift.

Consider two stationary observers X and Y in Figure, located

on either side of a stationary source. Each observer hears
the same frequency, and that frequency is the frequency
produced by the stationary source.
 A stationary source sends out sound waves at a constant
frequency Fs , with a constant wavelength

At the speed of sound v. Two stationary observers X and Y,

on either side of the source, observe a frequency Fo = Fs,
with a wavelength.

Now consider a stationary observer X with a source moving

away from the observer with a constant speed Vs < V
(Figure). At time
T = 0 , the source sends out a sound wave, indicated in
black. This wave moves out at the speed of sound v. The
position of the sound wave at each time interval of period
Ts , is shown as dotted lines. After one period, the source
has moved ΔX=VsTs and emits a second sound wave, which
moves out at the speed of sound. The source continues to
move and produce sound waves, as indicated by the circles
numbered 3 and 4. Notice that as the waves move out, they
remained centered at their respective point of origin.

A source moving at a constant speed Vs away from an

observer X. The moving source sends out sound waves at a
constant frequency Fs , with a constant wavelength

, at the speed of sound v. Snapshots of the source at an

interval of Ts are shown as the source moves away from the
stationary observer X. The solid lines represent the position
of the sound waves after four periods from the initial time.
The dotted lines are used to show the positions of thwaves
at each time period. The observer hears a wavelength of

Using the fact that the wavelength is equal to the speed

times the period, and the period is the inverse of the
frequency, we can derive the observed frequency:Now

consider a source moving at a constant velocity Vs,

moving toward a stationary observer Y, also shown in
Figure. The wavelength is observed by Y as

Once again, using the fact that the wavelength is equal to

the speed times the period, and the period is the inverse of
the frequency, we can derive the observed frequency:
When a source is moving and the observer is stationary, the
observed frequency is

Where Fo is the frequency observed by the stationary

observer, Fs is the frequency produced by the moving
source, v is the speed of sound, Vs is the constant speed of
the source, and the top sign is for the source approaching
the observer and the bottom sign is for the source
departing from the observer.
Where Fo is the frequency observed by the stationary
observer, Fs is the frequency produced by the moving
source, v is the speed of sound, Vs is the constant speed of
the source, and the top sign is for the source approaching
 the observer and the bottom sign is for the source
departing from the observer.

What happens if the observer is moving and the source is

stationary? If the observer moves toward the stationary
source, the observed frequency is higher than the source
frequency. If the observer is moving away from the
stationary source, the observed frequency is lower than the
source frequency. Consider observer X in Figure as the
observer moves toward a stationary source with a speed
Vo. The source emits a tone with a constant frequency Fs
and constant period Ts. The observer hears the first wave
emitted by the source. If the observer were stationary, the
time for one wavelength of sound to pass should be equal
to the period of the source Ts.Since the observer is moving
toward the source, the time for one wavelength to pass is
less than Ts and is equal to the observed period

At time T=0, the observer starts at the beginning of a

wavelength and moves toward the second wavelength as the
wavelength moves out from the source. The wavelength is
equal to the distance the observer traveled plus the distance
the sound wave traveled until it is met by the observer:
A stationary source emits a sound wave with a constant
frequency Fs , with a constant wavelength
 Moving at the speed of sound v. Observer Y moves away
from the source with a constant speed Vo , and the figure
shows initial and final position of the observer Y. Observer
Y observes a frequency lower than the source frequency.
The solid lines show the position of the waves at T=0 . The
dotted lines show the position of the waves at t= To.

If the observer is moving away from the source (Figure), the

observed frequency can be found:
A stationary source emits a sound wave with a constant
frequency Fs, with a constant wavelength

Moving at the speed of sound v. Observer Y moves away from

the source with a constant speed Vo , and the figure shows
initial and final position of the observer Y. Observer Y observes
a frequency lower than the source frequency. The solid lines
show the position of the waves at T=0 . The dotted lines show
the position of the waves at t = To.
The equations for an observer moving toward or away from a
stationary source can be combined into one equation

Where Fo is the observed frequency, Fs is the source

frequency, Vw is the speed of sound, Vo is the speed of the
observer, the top sign is for the observer approaching the
source and the bottom sign is for the observer departing from
the source.
Figure and Figure can be summarized in one equation (the
top sign is for approaching) and is further illustrated in
Figure:

Where Fo is the observed frequency, Fs is the source

frequency, Vw is the speed of sound, Vo is the speed of the
observer, Vs is the speed of the source, the top sign is for
approaching and the bottom sign is for departing.