Doppler Effect – Formula, Cases & Applications | Entrance Exam Physics Notes

DOPPLER EFFECT – SHORT NOTES (Entrance Exam Point of View)

1. Definition

The apparent change in frequency (or wavelength) of sound/light due to relative motion between the source, observer, and medium is called the Doppler Effect.

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2. Doppler Effect for Sound (Most Important for Exams)

General Formula

$$f^{\mathrm{\prime }}=f\left(\frac{v\pm v_o}{v\mp v_s}\right)$$

Where:

• $f'$ = apparent frequency

• $f$ = actual frequency

• $v$ = speed of sound

• $v_o$ = observer speed

• $v_s$ = source speed

Sign Convention (VERY IMPORTANT)

• Observer moving toward source → use + in numerator

• Observer moving away → use –

• Source moving toward observer → use – in denominator

• Source moving away → use +

Closer → Higher frequency
Farther → Lower frequency

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3. Special Cases

Case 1: Stationary Observer, Moving Source

$$f^{\mathrm{\prime }}=f\left(\frac{v}{v\mp v_s}\right)$$

• Source approaches → frequency increases

• Source recedes → frequency decreases

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Case 2: Moving Observer, Stationary Source

$$f^{\mathrm{\prime }}=f\left(\frac{v\pm v_o}{v}\right)$$

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Case 3: Both Moving Same Direction

Use general formula.

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4. No Doppler Effect When

• Source and observer both move with same velocity and direction

• Motion perpendicular to line joining source & observer (in sound)

• In vacuum (for sound)

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5. Doppler Effect for Light (Relativistic) – JEE Advanced Only

$$f^{\mathrm{\prime }}=f\sqrt{\frac{1-\beta }{1+\beta }}$$

where $\beta = \frac{v}{c}$

• Only depends on relative motion, no medium involved.

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6. Applications (High Probability Questions)

• Radar and speed guns

• Astronomy (red shift / blue shift)

• Ultrasound scanning

• Weather Doppler radar

• Siren of ambulance/fire truck

• Moving trains, horns, vehicles

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7. Red Shift & Blue Shift

• Red Shift: source moves away → frequency decreases → wavelength increases

• Blue Shift: source moves toward → frequency increases → wavelength decreases

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8. Important Notes

• Doppler shift is maximum when motion is along the line of sight

• No frequency change if source/observer moves perpendicular

• In wind: only speed of sound changes (modify v → v ± wind speed)

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