Doppler Shift

You can notice the Doppler effect when an ambulance or a fire engine passes by with its sirens blaring. The siren’s pitch suddenly drops the moment the ambulance starts to move away from you. Another effect you can hear is how the siren’s sound suddenly becomes markedly quieter as soon as the ambulance passes.

In this example, the observer and air are at rest while the sound source, the ambulance, moves with the speed V. This gives the same effect as if the sound source were at rest and the observer and air were moving at the same speed but in the opposite direction.

Model Definition

This is an axisymmetric problem with a point source at rest at the origin, (r, z) = (0, 0), emitting spherical sound waves with the frequency f = 100 Hz. The surrounding air moves at V = 50 m/s (180 km/h or roughly 112 miles/hour) in the negative z direction. With this setup, the rz-plane is the horizontal plane at the level of the source and the observer, and the effects of reflections at the ground are neglected.

Assume, furthermore, that the observer stands 1 m from where the ambulance passes by. In the model geometry, this situation amounts to the observer moving with the flow along the line r = 1.

The boundary conditions are absorbing because there is no physical boundary around the source. This is modeled using perfectly matched layers.

Results and Discussion

The acoustic wavelength decreases for a wavefront moving in the opposite direction of the airflow. This situation corresponds to the approach stage of the ambulance, which, for the stationary observer on the ground, implies a perceived frequency that is higher than the nominal source frequency f. Conversely, the wavelength increases and the perceived frequency decreases when the acoustic wave moves with the flow during the departing stage. These two stages correspond, respectively, to the solid and dashed curves in Figure 1.

Figure 1: The x-axis represents the distance between the ambulance and the point where it passes the observer. The solid line shows the pressure perceived by the observer as the ambulance is moving toward it. The dashed line shows the pressure as the ambulance is moving away from the observer.

An inspection of Figure 1 also shows that the amplitude drops off at a faster rate when the ambulance is moving away from the observer than when it is moving toward it. This effect is also visible in Figure 2 and Figure 3, which both show the sound pressure level.

Figure 2: Sound pressure level around the point source, represented by colors and contour lines. Note how the outermost contour runs from well inside the physical domain to the PML, showing that the sound is greater below than above the source.

Figure 3: Sound pressure level at the observer’s position during the ambulance’s approach (solid, blue line) and departing (dashed, green line) versus distance from the position (r, z) = (1 m, 0)(where the observer-ambulance distance is the smallest).

Acoustics_Module/Aeroacoustics_and_Noise/doppler_shift

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Define parameters for the background flow conditions, the signal frequency, and the geometry.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
V	50[m/s]	50 m/s	Ambulance speed
f0	100[Hz]	100 Hz	Signal frequency
R0	20[m]	20 m	Computational domain radius
dRpml	2[m]	2 m	PML thickness