Doppler effect — all cases - source moving, observer moving, both

1.6.21 · Physics › Oscillations & Waves

Frequency change KYUN hoti hai?

Ek sound source ek crest emit karta hai, phir ek period $T$ wait karta hai agla emit karne se pehle. Us time mein pehla crest bahar ki taraf travel kar chuka hota hai. Jo frequency tum sunते ho woh bas yeh hai:

$f^{'} = \frac{number of crests passing you}{time} = \frac{speed of crests relative to you}{distance between crests (the wavelength you meet)}$

Toh hume sirf do cheezein track karni hain:

Medium mein wavelength (tab badalti hai jab source move kare — woh apni khud ki waves ko chase karta hai).
Woh speed jis par crests tumhare paas se sweep karti hain (tab badalti hai jab observer move kare).

Neeche sab kuch inhi do effects ki bookkeeping hai. $v$ = medium mein wave ki speed (e.g. sound $\approx 340$ m/s). Medium referee hai — saari speeds usi ke relative mein measure hoti hain.

Har case ko scratch se derive karna

Case 1 — Observer move kare, source still

Medium mein wavelength unchanged rehti hai: $λ = v / f$ (source kuch chase nahi kar raha). Lekin agar observer source ki taraf $v_{o}$ speed se move kare, toh crests $v + v_{o}$ speed se sweep hoti hain (tum unse khud milने jaate ho).

$f^{'} = \frac{relative speed of crests}{λ} = \frac{v + v _{o}}{v / f} = f \frac{v + v _{o}}{v}$

Yeh step kyun? Frequency = (crests kitni tezi se tumhare paas aati hain) ÷ (unke beech spacing). Spacing $λ$ fixed hai; sirf approach speed badi.

Door jaana: $+ v_{o} \to - v_{o}$ replace karo.

Case 2 — Source move kare, observer still

Ab source apni hi waves ko chase karta hai. Ek period $T$ mein woh tumhari taraf $v_{s} T$ move karta hai, toh agla crest kareeb se emit hota hai — tumhari taraf wavelength compress hoti hai:

$λ^{'} = λ - v_{s} T = \frac{v}{f} - \frac{v _{s}}{f} = \frac{v - v _{s}}{f}$

Yeh step kyun? Har crest pichhle se $v_{s} T$ kareeb se janam leta hai, toh gap exactly utna hi kam hota hai.

Crests phir bhi medium mein $v$ speed se travel karti hain (medium wave speed set karta hai, source nahi). Toh:

$f^{'} = \frac{v}{λ ^{'}} = f \frac{v}{v - v _{s}}$

Source receding: $- v_{s} \to + v_{s}$ .

Case 3 — DONO move karein (master formula)

Combine karo: observer crests ki approach speed change karta hai; source wavelength change karta hai. Dono stack karo:

$f^{'} = f \frac{v \pm v _{o}}{v \mp v _{s}}$

Figure — Doppler effect — all cases - source moving, observer moving, both

Worked Examples

Common Mistakes (steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho tum apne dost ko har second ek ball throw kar rahe ho. Agar tumhara dost tumhari taraf bhaage, woh balls zyada baar pakadega → "higher frequency." Agar tum throw karte waqt dost ki taraf chalo, har ball usse kareeb se chodti hai, toh balls bunch ho jaati hain — woh phir bhi unhe zyada baar pakadta hai. Sound crests woh balls hain. Kisi bhi tarah se kareeb aana = zyada tezi se pakadna = zyada pitch. Door jaana = dheere = kam pitch (ambulance ka tone giarna jab woh guzar jaaye).

Flashcards

Master Doppler formula for sound

f^{'} = f \frac{v \pm v _{o}}{v \mp v _{s}}

, signs chosen so approach raises pitch.

Why does a moving SOURCE change frequency?

Woh apni waves ko chase karta hai, wavelength compress/stretch karta hai:

λ^{'} = (v \mp v_{s}) / f

Why does a moving OBSERVER change frequency?

Woh crests sweep karne ki speed change karta hai: relative crest speed

= v \pm v_{o}

, jabki

λ

fixed rehta hai.

Which speed goes in the numerator?

Observer ki speed

v_{o}

(hamesha upar).

Which speed goes in the denominator?

Source ki speed

v_{s}

(hamesha neeche).

Sign when observer moves toward source

Numerator mein

+ v_{o}

(

f^{'}

badhata hai).

Sign when source moves toward observer

Denominator mein

- v_{s}

(

f^{'}

badhata hai).

What is the reference frame for all speeds?

Medium (e.g. still air); medium wave speed

v

set karta hai.

What happens when

v_{s} \to v

Denominator

\to 0

f^{'} \to \infty

: wavefronts pile up hokar shock wave / sonic boom banti hai.

Observer still, source receding at

v_{s}

f^{'}

f^{'} = f \frac{v}{v + v _{s}}

(lower pitch).

Is source-toward equal to observer-toward at same speed?

Nahi — alag mechanisms hain; yeh sirf kam speeds par approximately agree karte hain.

Effect of wind speed

w

toward observer?

Numerator aur denominator dono mein

v \to v + w

replace karo (medium drift karta hai).

Connections

Wave speed in a medium — $v$ set karta hai; source ise change nahi kar sakta.
Wavelength and frequency relation — $λ = v / f$ poori derivation ki neenv hai.
Sonic boom and shock waves — $v_{s} \geq v$ limit.
Relative velocity — observer-frame crest speeds.
Doppler effect of light — relativistic version, koi medium nahi, poori tarah symmetric.
Beats — jab do Doppler-shifted tones combine hote hain tab kya sunते ho.

Doppler effect — all cases - source moving, observer moving, both

Frequency change KYUN hoti hai?

Har case ko scratch se derive karna

Case 1 — Observer move kare, source still

Case 2 — Source move kare, observer still

Case 3 — DONO move karein (master formula)

Worked Examples

Common Mistakes (steel-manned)

Flashcards

Connections

Concept Map

Deep Dive