e-Doppler Effect 1

Doppler Effect 1 — What Happens When the Sound Source Moves and There Is Wind? —

　　　Wavelength Display 　Frequency Display 　Velocity Vector Display
Source Frequency f: 　Source Velocity vs: 　Wind Velocity vw:

Description :

This page is designed to deepen your understanding of the Doppler effect when the sound source is moving and when there is wind.
    A tuning-fork-shaped sound source is placed at the center, with observers positioned on the left and right. 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.
    When the sound source moves, the center of each newly generated spherical wavefront also moves, allowing you to observe how the spacing between adjacent wavefronts (the wavelength) changes. You can also explore the case in which wind is present and the air, which acts as the medium transmitting sound, moves uniformly.
    By trying various values of the source frequency, source velocity, and wind velocity, deepen your understanding of how the wavelength changes and how the observed sound frequency is affected.
(Hint)
Check Velocity Vector Display, and generate wavefronts using the " 1 s >| " step mode. From the displayed diagram, consider how the wavelength can be determined.
(Note 1)
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 source velocity vs is a quantity that includes direction as well as magnitude. When it is negative, it indicates motion in the negative x-direction with speed |vs|, and may also be written as −|vs|.Accordingly, when the sound source moves in the negative direction, V − vs means V + |vs|. The same applies to the wind velocity vw.
(Note 2)
The wavelength of the wave emitted to the right from the source is denoted by λ' , and that of the wave emitted to the left by λ''. These wavelengths λ' and λ'' appear in the formulas used to determine the frequencies f' and f'' observed by observers on the right and left, respectively. However, since these wavelengths are the wavelengths at the observers’ positions, there is a time delay before changes in the wavelength at the source are reflected in the frequencies observed by the observers.

● “ > ”: 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. You can control the time progression using these buttons.
● 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 “Source Velocity vs” slider, you can change the velocity of the sound source. Motion to the right is taken as positive, and motion to the left as negative. The initial value is 0.4 times the sound speed V, that is, 0.4 V. It can be adjusted within the range from −1.2 V to 1.2 V.
● With the “Wind Velocity vw” slider, you can change the wind velocity. Motion to the right is taken as positive, and motion to the left as negative. The initial value is 0, corresponding to no wind, and it can be adjusted within the range from −0.5 V to 0.5 V. The motion of the air due to the wind can be seen from the movement of the balloon.
● By checking the “Wavelength Display” checkbox, the wavelength of the waves emitted from the sound source is displayed as a multiple of the wavelength λ when the source is stationary. This is shown for both right- and left-traveling waves relative to the sound source.
● By checking the “Frequency Display” checkbox, the frequency of the waves received by the observers is displayed both as a multiple of the source frequency f and in units of Hz. This is shown for both the left and right observers.
● By checking the “Velocity Vector Display” checkbox, the wave propagation velocity (red), the source velocity (blue), the wind velocity (light blue), and the vector representing the difference between the wave velocity and the source 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 source velocity is equal to the frequency, you can understand how the wavelength changes due to the Doppler effect and how the Doppler effect formula is derived.

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