e-Doppler Effect 2

Doppler Effect 2 — What Happens When the Observer Moves? —

　　　Frequency Display 　Velocity Vector Display
Source Frequency f: 　　Observer Velocity vo:

Description :

This page is designed to deepen your understanding of the Doppler effect when the observer is moving.
A tuning-fork-shaped sound source is placed on the left, and an observer is placed at the center. When you press the start button “ > ”, spherical wavefronts are generated successively from the sound source with frequency f. The wavefronts are normally displayed as blue circles, but every 1 s they are shown as red circles, so that you can see that a number of wavefronts equal to the frequency are produced in 1 s. In this simulation, there is no wind. Use the “Observer Velocity vo” slider to give the observer a velocity and set it in motion. As the observer moves, the number of wavefronts received by the observer per second changes, allowing you to see that the observed frequency also changes. Try various cases and deepen your understanding of how the observed frequency varies.
(Hint)
When you press the “ t = 2 s ” button, the simulation stops at the moment when the first wavefront just reaches the observer. Then check Velocity Vector Display, and generate wavefronts using the “ 1 s >| ” step mode. By counting the number of wavefronts that reach the observer in the displayed diagram, consider how the observed frequency can be determined.
(Note)
The sound speed V represents the magnitude of sound and is always taken to be a positive value, such as 340 m/s. Therefore, the velocity of sound traveling in the positive x-direction is V, while that traveling in the negative direction is represented as −V.
In contrast, the observer velocity vo is a quantity that includes both magnitude and direction. When it is negative, it indicates motion in the negative x-direction with speed |vo|, and may also be written as −|vo|. Accordingly, when the observer moves in the negative direction, V − vo means V + |vo|.

● “ > ”: Start (real time), “ Slow ) ”: Slow motion (time advances at one-fifth speed), “ || ”: Stop, “ >| ”: Step forward by 0.05 s, “ 1 s >| ”: Step forward by 1 s, “ t = 0 ”: Time reset, “ t = 2 s ”: Set the time to when the first wavefront reaches the observer. These buttons allow you to control the time progression.
● With the “Source Frequency f” slider, you can change the frequency of the sound source in units of Hz. The initial value is 5 Hz, and it can be adjusted within the range from 1 Hz to 10 Hz.
● With the “Observer Velocity vo” slider, you can change the velocity of the observer. Motion to the right is taken as positive, and motion to the left as negative. The initial value is 0, corresponding to the observer at rest. Taking the sound speed as V, the velocity can be adjusted within the range from −0.9 V to 0.9 V.
● By checking the “Frequency Display” checkbox, the frequency observed by the observer is displayed both as a multiple of the frequency f observed when the observer is stationary and in units of Hz.
● By checking the “Velocity Vector Display” checkbox, the wave propagation velocity (red), the observer velocity (green), and the vector representing the difference between the wave velocity and the observer velocity (yellow) are displayed. The lengths of the vectors are drawn to represent the distance traveled in 1 s. Since the number of wavefronts along the vector representing the difference between the wave velocity and the observer velocity corresponds to the number of wavefronts observed by the observer, you can understand the change in frequency due to the Doppler effect and how the Doppler effect formula is derived.

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