Waves chapter mein wave equation, superposition, standing waves, beats aur Doppler effect aate hain — Class 11 Physics ka last scoring chapter. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.
Important Formulas & Concepts — Waves
- v = fλ; y = A·sin(kx − ωt)
- k = 2π/λ; ω = 2πf
- String wave speed: v = √(T/μ)
- Sound speed: v = √(γP/ρ); air mein ~343 m/s (20°C)
- Beats frequency = |f₁ − f₂|
- String: fₙ = nv/2L
- Open pipe: fₙ = nv/2L (all harmonics); closed pipe: fₙ = nv/4L (odd only)
- Doppler: f2 = f(v ± v₀)/(v ∓ vₛ)
Quick Revision Points
- Transverse waves strings mein, longitudinal sound ke liye
- Node par displacement zero, antinode par maximum
- Closed pipe mein sirf odd harmonics
- Sound speed ∝ √T — temperature badhne par badhti hai
- Doppler: approach = frequency badhti hai, recede = ghatti hai
📘 Complete Visual Notes + Formula Sheet PDF
Ye sirf ek quick preview hai. Pura chapter — colour-coded mind-maps, saare derivations, solved formula sheet — instant PDF download.
FAQ
Doppler effect ke signs confuse hote hain?
PDF mein visual sign-map hai — approach vs recede ek nazar mein clear ho jata hai.
Ye chapter JEE mein kitna weightage rakhta hai?
Standing waves + Doppler se har saal 2-3 questions confirm.
Explore more: free sample notes, free calculators aur interactive simulators.