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Set the scope

These equations apply to sound or other mechanical waves travelling at speed $v$ through a medium. Assume the source and observer move along the straight line joining them, and treat one moving object at a time as required by the syllabus. They do not apply to electromagnetic waves.

\text{moving source: }f'=f\frac{v}{v\pm u_s}\qquad\text{moving observer: }f'=f\frac{v\pm u_o}{v}

Choose the sign from the motion

For a moving source, subtract $u_s$ when it approaches and add it when it recedes. For a moving observer, add $u_o$ when it approaches and subtract it when it recedes. This makes approach give $f'>f$ and separation give $f'<f$ .

Worked example — moving source

A $480\,\text{Hz}$ sound source approaches a stationary observer at $50.0\,\text{m s}^{-1}$ while sound travels at $350\,\text{m s}^{-1}$ . Use the source-toward sign: $f'=480[350/(350-50.0)]=560\,\text{Hz}$ . The result is above $480\,\text{Hz}$ , matching the approach check.

Keep the syllabus boundary

Use one moving object at a time and motion along the line joining source and observer. Keep every speed in the same units. These mechanical-wave equations do not apply to electromagnetic waves; reflected medical or radar signals may involve a shift on both outward and return paths.

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Source S produces sound waves of speed v and frequency f. S moves with constant velocity $\frac{v}{5}$ away from a stationary observer.

What is the frequency measured by the observer?

The HL extension is secure when you choose the mechanical-wave formula from the moving object and direction.

Moving source: f′=fv/(v±us)
Moving observer: f′=f(v±uo)/v
Approach gives f′>f; recession gives f′<f
These formulas are for sound or mechanical waves, not electromagnetic waves

C.5.5 (HL)—Mechanical-wave Doppler formulas

Apply Mechanical-Wave Doppler Formulas

Retrieve the HL C.5 Doppler Effect Model

C.5.5 (HL) Exam Analysis