JEE/NEET Physics · Oscillations & Waves series · Part 8 of 8 · All parts →
- Doppler: relative motion changes the heard frequency — closer = higher, receding = lower
- The size of the shift grows with (speed ÷ wave speed)
- Light version: redshift/blueshift — the universe’s speedometer
- Applications: sirens pass by, radar speed guns, exoplanets, expanding universe
- Complete chapter formula card at the end
An ambulance siren screams toward you, passes, and the pitch drops — the driver hears no change at all. That pitch shift, the Doppler effect, is how police catch speeders, doctors image blood flow, and astronomers discovered the universe is expanding. The finale of the Oscillations & Waves series.
- Why motion changes pitch
- The rule of thumb: closer = higher
- What each letter means
- Light: red and blue shifts
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap + formula card
Why Motion Changes Pitch
The siren emits crests at a fixed rate. Rushing toward you, each new crest starts from a closer position — crests arrive squeezed together (shorter λ, higher f). Moving away, each crest starts farther — crests arrive stretched (longer λ, lower f). The source never changed; the journey did.
The Rule of Thumb: Closer = Higher
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| f | heard frequency (what changes) | Hz |
| f₀ | true emitted frequency (fixed by source) | Hz |
| v | wave speed in the medium (sound: ~343 m/s in air) | m/s |
| v_s, v_o | source’s and observer’s speeds toward each other | m/s |
Full quantitative formulas fill a page; for exams, the honest shortcut is the ratio scale: a source at 10% of the sound speed shifts pitch by ~10% — roughly 1.7 musical semitones. Memorise direction + rough size; derive exactly when asked.
Light: Red and Blue Shifts
Light does the same, read in colours: approaching star = squeezed light = blueshift; receding = stretched = redshift. Edwin Hubble saw every distant galaxy redshifted — and that observation IS the expanding universe. The same siren physics, at cosmic scale.
Solved Examples
Direction rule: approaching — heard above 1000 Hz; the instant it passes, a drop to below 1000 Hz. The drop AT the pass is the signature. ✔
Answer: higher → drops to lower at the pass
Double shift: the car sees a raised frequency (approaching source), then re-radiates it as a moving source — total shift ≈ 2 × f₀ × (v/c) = 2 × 24×10⁹ × (30/3×10⁸).
= 4,800 Hz beat — the gun counts 4.8 kHz of beats and prints ‘108 km/h’. ✔
Answer: beat ≈ 4.8 kHz → 108 km/h
10% approach → ~10% up: ≈ 660 Hz.
Exact: f = 600 × 340/(340−34) = 600 × 340/306 ≈ 667 Hz — the shortcut’s 660 lands within 1%. Direction + ratio first, exact when needed. ✔
Answer: ≈ 667 Hz (exact); ~660 by the 10% rule
- Reversing the direction. Approach = higher, ALWAYS — for both moving source and moving observer. Write the direction rule before any formula.
- Using wave speed vs relative speed loosely. The shift scale is source speed ÷ WAVE speed (343 for sound, 3×10⁸ for light) — mixing them gives absurd answers.
- Thinking the siren itself changes. f₀ never changes; only the arrival rate does. The driver hears the true pitch throughout.
- Redshift = ‘redder colour’ only. Astronomically it means ‘stretched wavelengths’ — could start ultraviolet and still be called redshifted.
This Physics in Your Daily Life
- Every siren, horn and racing car that drops pitch as it passes is demonstrating Doppler publicly.
- Speed guns (and speed traps) read a double-Doppler beat — your speed ticket is a frequency count.
- Doppler ultrasound in hospitals measures blood-flow speed through the skin — no incision, pure echo physics.
- Weather Doppler radar maps wind inside storms by the shift of reflected microwaves — tornado warnings run on this card.
- The expanding universe: Hubble’s redshifts, the Big Bang’s evidence base, is the ambulance siron stretched across billions of light-years.
| What | Formula | Remember |
|---|---|---|
| SHM definition | a = −ω²x | pull-back ∝ displacement |
| SHM motion | x = A sin(ωt); v_max = Aω; a_max = ω²A | fastest at centre, strongest pull at ends |
| Clocks | pendulum: 2π√(L/g); spring: 2π√(m/k) | mass-free pendulum; gravity-free spring |
| SHM energy | ½kA² total; avg KE = avg PE | amplitude-squared |
| Springs combined | series k/2, parallel 2k (equal) | period ∝ 1/√k |
| Resonance | driver = natural frequency | amplitude maximum; damping barely shifts f |
| Wave link | v = fλ | f by source, v by medium |
| String waves | v = √(T/μ) | tighter/lighter = faster |
| Standing waves | f_n = n·v/2L (string, open pipe); odd only for closed (v/4L) | nodes λ/2 apart; ends are nodes |
| Beats | f_beat = |f₁ − f₂| | zero beats = tuned |
| Doppler | approach → higher; recede → lower | shift ∝ speed ÷ wave speed; light: red/blue |
Practice set (answers hidden — try first)
(NEET-level) A source approaches. The observer hears:
(NEET-level) A galaxy’s light is redshifted. It is:
(JEE Main-level) A car approaches a radar at 25 m/s; f₀ = 24 GHz. Beat ≈
(Concept) The siren driver hears:
(JEE Main-level) Source at 10% of sound speed, approaching. Heard pitch changes by about:
- 🧠 Chant: ‘closer means higher — passing means dropping’.
- 🧠 Scale rule: ‘10% of wave speed ≈ 10% pitch shift’.
- 🏠 Daily: every passing siren is a Doppler demonstration you can’t unhear.
- 🏠 Daily: speed tickets, blood-flow scans, tornado warnings, and the Big Bang — one effect, every scale.
- 🔁 Doppler shifts frequency, not the source
- 🔁 approach higher / recede lower
- 🔁 shift ∝ v_source/v_wave
- Doppler: relative motion shifts heard frequency
- approach = higher pitch; recede = lower — always
- shift size ∝ source speed ÷ wave speed
- light version: blueshift (approach), redshift (recede)
- radar guns = double Doppler; the beat is the speed
Quick revision
- Doppler: relative motion changes the heard frequency — closer = higher, receding = lower
- The size of the shift grows with (speed ÷ wave speed)
- Light version: redshift/blueshift — the universe’s speedometer
- Applications: sirens pass by, radar speed guns, exoplanets, expanding universe
- Complete chapter formula card at the end
- The rule of thumb: closer = higher
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