Acoustic Doppler Effect
1. Introduction
What is the Doppler effect? The most common example of this effect is the pitch of a siren of
a fire engine. We may have noticed, that as a fast moving siren passes by us, the pitch of the
siren sharply drops in pitch. In the beginning, when the siren is coming towards us, its pitch is
higher. After passing us, the siren is going away from us and the pitch becomes lower. This is
a appearance of the Doppler effect. Thus we may define, the Doppler effect as the change in
the observed frequency of a source due to the relative motion between the source and the
receiver. The relative motion that affects the observed frequency is only the motion in the
Line-Of-Sight (LOS) between the source and the receiver.
There are two diverse situations are possible for the Doppler effect. The first is when the
receiver is moving and the source is stationary. For example, we are in a moving car and are
passing by a stationary siren. Second situation is, when we (receiver) are stationary, and the
source is moving you. Although the second situation may be more common, yet the first is
easier to examine.
1.1 First Situation: Relative motion of the receiver
Suppose a source is stationary, as shown in the Figure 1 below, it will emit sound waves that
propagate out from the source. When the receiver moves towards the source, it will detect the
sound coming from the source. However, each successive sound wave will be detected earlier
that it would have, if the receiver were stationary, due to the motion of the receiver in the
LOS.
Figure 1
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Thus the frequency, that each successive wave front would be detected, would be changed by
this relative motion where:
Δ𝑓 =
v𝑟
𝜆0
Here:
λ0=original wavelength of the source
Δf=change in the observed frequency
vr=velocity of the receiver in the LOS
Since the original frequency of the source can be expressed in terms of the wavelength where,
f0=c/λ0, the observed frequency becomes:
𝑓 ′ = 𝑓0 + Δ𝑓
𝑐 vr
𝑓′ = +
𝜆0 λ0
𝑐 + v𝑟
)
𝑐
𝑓 ′ = 𝑓0 (
It is worth mentioning that the above equation only works if the relative velocity of the
receiver, vr is towards the source. If the relative motion is away from the source, the relative
velocity would be in the opposite direction and the equation will take the form:
𝑐 − v𝑟
)
𝑐
𝑓 ′ = 𝑓0 (
Together the two equations for the observed frequency can be expressed as:
𝑓 ′ = 𝑓0 (
𝑐 ± v𝑟
)
𝑐
1.2 Second Situation: Relative motion of the source
When the source is moving towards the receiver, the effect is somewhat different. The
spacing between the successive wave fronts would be less as seen in the Figure 2 shown
below. It is expressed as:
Δ𝜆 =
Where, vs = relative velocity of the source
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v𝑠
𝑓0
Figure 2
Observed frequency in this situation can be expressed as:
𝑐
𝑓′ =
(𝜆0 + Δ𝜆)
𝑐
𝑓 ′ = 𝑓0 (
)
𝑐 − v𝑠
It is important to note that the above expression is valid, when the source is moving towards
the receiver. However, if the source is moving away from the receiver, the equation would
become:
𝑓 ′ = 𝑓0 (
𝑐
)
𝑐 + v𝑠
Collectively, the two equations for the observed frequency can be expressed as:
𝑓 ′ = 𝑓0 (
𝑐
)
𝑐 ∓ v𝑠
While comparing the two equations of the observed frequency, it is important to note that in
the second situation, the plus/minus symbol is inverted, since the sign on the top should be
used for the relative motion of the source towards the receiver.
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1.3 Doppler Equation
By combining the two equations of the observed frequency, we may arrive at one equation
that is termed as Doppler equation. Expression for this equations is:
𝑓 ′ = 𝑓0 (
𝑐 ± v𝑟
)
𝑐 ∓ v𝑠
We should be cautious about the the velocity of the receiver, vr and the velocity of the source
vs. These are only the magnitude of the relative velocities in or along the LOS. In other
words, the component of the velocity of the source and the receiver, that are perpendicular to
the LOS do not change the received frequency. Secondly, the top sign in the numerator and
the denominator are the sign convention to be used when the relative velocities are towards
the other. If the source is moving towards the receiver, the sign that must be used in the
denominator would be the minus sign. If the source is moving away from the receiver, the
sign must be used would be the plus sign.
2. Objectives of the Experiment
To study the propagation of sound waves and Doppler shift in frequency. Frequency changes
will be measured and analysed for different relative velocities of source and receiver.
3. Description of the equipment
Figure 3 shows the experimental setup for the moving receiver and the sound source at rest.
This set up consist of:

Cobra3 basic unit

Power supply, 12V

RS232 data cable

Cobra3 timer/counter software

Microphone

Battery, 9V, 6F 22 DIN 40871

Function generator

Stand tube

Sound head

Plug with socket and cross-hole

Screen with plug
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
Support rod, stainless steel

Light barrier, compact

Track, l=900mm

Car, motor driven

DC power supply

Barrel base, -pass-

Boss head

Support

Connecting cords

PC, windows 95 or higher
Figure 3
4. Experimental Procedure

Make the experimental set up as shown in Figure 3.

Now make connections as shown in the circuit diagram in Figure 4.

Turn on PC and other equipment of the experimental set up.

Set the function generator to desired frequency. For example we may choose 16000
Hz to be emitted from the sound source (loudspeaker).

Open the PHYWE software in the PC and start the Cobra3 time/counter program and
set the parameters for the frequency measurement in accordance with Figure 5.
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Figure 4
Figure 5
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Figure 6

After fixing the function generator at desired frequency, place the car with the
microphone in the vicinity of the loud speaker and measure the frequency at rest f0
several times. To do this, click the start button on the PC screen and the counter
program will display some frequency having value nearly identical as produced by the
function generator.

Set the velocity controller on the car to an intermediate position and set the direction
of movement in such a manner that the car moves towards the loudspeakers. Release
the car and click the start button, when the car’s velocity has become constant. i.e. it is
no longer accelerating. Repeat the entire procedure several times and note the
measured frequency in the observation Table1.

Further, repeat the above step, when the car moves away from the loudspeakers and
note the measured frequency in the observation Table1.

Now set the PHYWE measure software for the velocity measurement showing the
initial parameters in the timer program, according to Figure 6.

Do not change the velocity controller or the direction of movement of car with respect
to the previous partial experiment. Release the car and ensure that the screen passes
through the light barrier after the car’s velocity has become constant. Repeat the entire
procedure several times and note the values of velocity in observation Table 1.

Further, repeat the above step, when the car moves towards the loudspeakers and note
down the values of velocity in observation Table 1.
5. Results
The measured values for the frequency and velocity are listed in Table 1.
Here we are assuming:
c=340 m/s
Observed value of f0
f0=15984 Hz
Further, fcalculated can be obtained by the equation, mentioned in section 1.1:
𝑓 ′ = 𝑓0 (
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𝑐 ± v𝑟
)
𝑐
Table 1:
S. No.
Frequency (fmeasured) (Hz)
Moving towards Moving
Velocity (vr) (m/s)
away Moving
towards Moving away from
the source
from the source
the source
the source
1.
15987
15979
0.088
0.078
2.
15988
15980
0.085
0.076
3.
15985
15979
0.082
0.071
4.
15986
15978
0.082
0.071
5.
15988
15980
0.084
0.073
Mean
15987
15979
0.0842
0.0738
fcalculated
15988
15981
(Hz)
6. Observations from the Experiment:

It was observed from the calculated and measured values of the frequency (f’) that the
frequency increases when receiver is moving towards the source.

Calculated and measured values of the frequency (f’) show that the frequency
decreases when receiver is moving away from the source.
7. Important points to remember:

If the device does not measure the frequency despite clearly audible tone, it may be
necessary to adapt the output voltage of the microphone amplifier to the volume of the
loud speaker.

The function generator requires a warm-up period that is approximately 10 minutes
long. Subsequent to this period it provides a sinus tone at a stable frequency.

During the measurement no background noise may occur, since they would also be
registered by the microphone could falsify the measurement.

If several progressively smaller car velocities are successively measured, although the
position of the velocity controller has not been changed, this indicates this that there
are probably weak batteries in the car. Replace the batteries.

The fact that the cars forward and backward velocities differ slightly from each other
for the same velocity setting is normal and is due to the type of drive used in the car.
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