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

1.6.21 · D1 · Physics › Oscillations & Waves › Doppler effect — all cases - source moving, observer moving

Isse pehle ki hum master formula $f^{\prime }=f\frac{v\pm v_o}{v\mp v_s}$ ko padh bhi sakein, humein iske har letter ko samajhna hoga. Neeche, har symbol ek picture se bana hai, ek aisi order mein jahan har ek symbol sirf apne pehle waale symbols par depend karta hai.

1. Ek "crest" aur ek "wavefront" — woh cheez jo actually move karti hai

Ek loudspeaker hawa ko aage dhakelta hai, phir wapas kheechta hai, baar baar. Har push ek patli shell create karta hai jisme hawa squeeze hoti hai — ek crest. Yeh shells pond mein ripples ki tarah bahar ki taraf udte hain.

Figure dekho: source beech mein baitha hai, aur crests ko evenly spaced rings ke roop mein draw kiya gaya hai. Tumhara kaan har baar ek "tick" count karta hai jab bhi ek ring usse guzarti hai. Woh count-per-second hi pitch hai. Is picture ko yaad rakho — baad ke har symbol iske kisi hisse ka label hai.

2. Frequency $f$ — kitni baar crests paida hoti hain

Topic ko iske zaroorat kyun hai? Kyunki $f$ baseline hai — woh pitch jo tum suno agar koi move na kare. Poora Doppler question yeh hai: heard pitch $f^{\prime }$, is $f$ se kaise alag hai?

Dekho Wavelength and frequency relation partner idea ke liye.

3. Period $T$ — do crests ke beech ka intezaar

Humein $T$ ki zaroorat hai kyunki source moving effect exactly ek period mein measure hota hai — woh distance jo source next crest emit karne ke intezaar mein travel karta hai.

4. Wave speed $v$ — crests hawa mein kitni tez chalti hain

Figure ek aisa source dikhata hai jo daayein move kar chuka hai — lekin notice karo har crest ring abhi bhi uhi se same $v$ par expand ho rahi hai jahan woh paida hui thi. Rings off-centre hain, phir bhi har ek same rate se grow karti hai.

5. Wavelength $\lambda$ — crests ke beech ka gap

$\lambda$ exist kyun karna chahiye? Kyunki "kitni baar crests tumse takraate hain" $=$ "kitni tez aate hain" $÷$ "kitne door door hain." Yeh division is poore topic ka dhadakta dil hai:

Is formula ko aise padho: crests zyada tezi se aate hain (bada $v$) ya zyada pack hote hain (chhota $\lambda$) ⟹ higher frequency. Do Doppler mechanisms exactly yahi hain "tumhare liye $v$-as-seen-by-you badlo" aur "$\lambda$ badlo."

6. Heard frequency $f^{\prime }$ — yeh poora topic kya solve karta hai

Poora Doppler formula ek machine hai jo $f$ leta hai aur $f^{\prime }$ nikalta hai.

7. Do moving-speeds: $v_s$ aur $v_o$

Ab woh players jo stillness tod dete hain.

Figure dono effects ko side by side alag karta hai: left panel mein, source ka move karna front side par rings ko squeeze karta hai (chhota $\lambda$); right panel mein, observer ka move karna matlab crests ka crossing zyada tezi se aata hai even though rings evenly spaced hain.

8. Signs: $\pm$ aur $\mp$ — plus-or-minus padhna

Yeh foundations topic ko kaise feed karte hain

Upar se neeche padho: crest picture humein $f$, $\lambda$ aur $v$ deta hai; woh combine hokar $f=v/\lambda$ bante hain; do moving-speeds $v_s,v_o$ jodne se woh heard $f^{\prime }$ ban jaata hai; aur sign rule master formula finish karta hai.

Equipment checklist

Connections

• Wave speed in a medium — $v$, the referee speed define karta hai.
• Wavelength and frequency relation — $f=v/\lambda$ backbone.
• Relative velocity — crests ki speeds ek moving observer ko kaise dikhti hain.
• Sonic boom and shock waves — $v_s\to v$ limit kya ban jaata hai.
• Doppler effect of light — no-medium, symmetric cousin.
• Beats — do Doppler-shifted tones combine hote hain.
• Parent: Doppler — all cases