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Doppler-Shifted Frequency

The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave (or other periodic event) for an observer moving relative to its source.

The ratio of the frequency observed to the frequency of the wave emitted is the speed of sound in the medium plus the relative velocity of the observer divided by the speed of sound in the medium plus the relative velocity of the source.

Formula

QuantityVariable[Subscript["f", "o"], "Frequency"]/QuantityVariable[Subscript["f", "s"], "Frequency"] == (QuantityVariable["c", "SoundSpeed"] + QuantityVariable[Subscript["v", "o"], "Speed"] - QuantityVariable[Subscript["v", "w"], "Speed"])/(QuantityVariable["c", "SoundSpeed"] + QuantityVariable[Subscript["v", "s"], "Speed"] - QuantityVariable[Subscript["v", "w"], "Speed"])

symbol description physical quantity
fo frequency observed "Frequency"
fs frequency at the source "Frequency"
c sound speed "SoundSpeed"
vo speed of the observer toward the source "Speed"
vw wind speed "Speed"
vs speed of the source away from the observer "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Doppler-Shifted Frequency"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Doppler-Shifted Frequency"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Doppler-Shifted Frequency"], {QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("o"\)]\),"Speed"] -> Quantity[0, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("s"\)]\),"Speed"] -> Quantity[10, ("Meters")/("Seconds")]}]
Out[3]=

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