Doppler Shift as Function of MUSIC

[peterblair]

Hello, the internet.

I am attempting to graph Doppler Shift as a function of time for a music project. The equation for observed frequency is:

fo=fs(c)/vs(c)

Where
fo is observed frequency
fs is the source frequency
c is the speed of sound
vs is the velocity of the source

But when working with this equation I became confused: The entire point of the Doppler Shift is that the frequency changes over time, but time seems to be represented nowhere in this equation. So, at what point in time, or alternatively how far away from the listener is this equation measuring?

Also, can someone provide me with an equation that could graph fo as a function of time?

Thanks!

 

[Yanick]

The Doppler shift doesn't change with time, it changes with a change in some of the parameters of the equation you have listed.

For example consider a speaker on a moving platform with a stationary observer. As long as the speaker's speed and direction of travel remain constant, the Doppler shift will be constant in time. In other words if you were to plot observed frequency as a function of time it would be a horizontal line crossing the y-axis at whatever observed frequency you measure.

 

[mikeph]

You can graph it if you know v_s. That's where your time dependence is coming from: the moving source.

 

[dauto]

Hello, the internet.

I am attempting to graph Doppler Shift as a function of time for a music project. The equation for observed frequency is:

fo=fs(c)/vs(c)

Where
fo is observed frequency
fs is the source frequency
c is the speed of sound
vs is the velocity of the source

But when working with this equation I became confused: The entire point of the Doppler Shift is that the frequency changes over time, but time seems to be represented nowhere in this equation. So, at what point in time, or alternatively how far away from the listener is this equation measuring?

Also, can someone provide me with an equation that could graph fo as a function of time?

Thanks!

That equation doesn't look right to me. It should be [tex]f_o=\frac{c+v_o}{c+v_s}f_s,[/tex] where [itex]v_o[/itex] is the velocity of the observer and the other variables are as defined by the OP.

 

[PJC01]

Hello there,

I can understand your confusion about the equation for observed frequency and its representation of time. The equation you have provided is the basic equation for the Doppler Shift, but it does not explicitly include time as a variable. However, time is still a factor in this equation, as it is indirectly represented by the velocity of the source (vs). This velocity is measured in distance per unit time, so as the source moves, the frequency observed by the listener will change over time.

To graph fo as a function of time, you can use the following equation:

fo(t) = fs(c)/(c +/- vs*t)

Where t represents time and the +/- sign depends on the direction of the source's movement (towards or away from the listener). This equation takes into account the changing velocity of the source over time and can be used to plot a graph of observed frequency against time.

I hope this helps with your music project. Best of luck!