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

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.

How it is assessed

Questions calculate a received sound frequency for a moving source or observer, and may apply the shift twice when a reflected signal returns to the detector.

Command terms

Determine / What is

What earns marks

First identify whether the source or observer moves, choose the matching formula and sign from the direction, then check that approach raises and recession lowers the received frequency.

Watch for

Using the observer formula for a moving source, choosing the sign from the source’s absolute direction rather than toward/away from the observer, or forgetting a second shift after reflection.

Representative question

[Maximum number: 1]

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?

$\frac{4}{5} f$

$\frac{5}{6} f$

$\frac{6}{5} f$

$\frac{5}{4} f$

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

C.5.5 (HL) Exam Analysis

Assessment in practice

Retrieve the HL C.5 Doppler Effect Model

Question 1