1.6.14
Ek wave ek pattern hai jo ek saath do tareekon se repeat hota hai : woh space mein repeat hota hai (tum dekh sakte ho ki har kuch metres mein same shape aa rahi hai) aur woh time mein bhi repeat hota hai (ek jagah par, medium upar-neeche ek regular beat pe hilta rehta hai). Har wave parameter bas inn repetitions mein se kisi ek ka naam hai, ya phir kitna bada wiggle hai iska.
Space mein repetition → wavelength λ
Time mein repetition → period T frequency f
Wiggle ki size → amplitude A
Pattern kitni tez travel karta hai → wave speed v
Definition Paanch parameters
Amplitude A — kisi particle ki uski equilibrium position se maximum displacement. Units: metres (ya jo bhi medium ki displacement mein measure hota ho). Yeh middle line se ek distance hai, peak-to-peak NAHIN.Wavelength λ — woh sabse chhoti distance (metres mein) jis par wave shape repeat hoti hai. Crest-to-crest, ya trough-to-trough.Period T — kisi bhi ek particle ke ek poore oscillation ka time (seconds); iska matlab yeh bhi hai ki wave ek wavelength aage badhne mein kitna time leta hai.Frequency f — ek second mein poore oscillations ki sankhya. Units: hertz, 1 Hz = 1 s − 1 Wave speed v — woh speed (m/s) jis par fixed phase ka ek point (jaise koi ek crest) medium mein aage badhta hai.
f = 1/ T T 1 second mein 1/ T
Intuition WHY yeh sach hona hi chahiyeSpeed = distance ÷ time. Ek period T mein, ek crest aage exactly ek wavelength λ badhti hai (kyunki ek poore oscillation ke baad pattern bilkul same dikhta hai, bas λ
Intuition Ek subtle lekin zaroori baatKisi diye gaye medium mein wave ke liye, v f λ inversely linked hain: λ = v / f nahin badlti.
Worked example Example 3 — period aur amplitude seEk buoy kul 1.2 m 4 s 3 m/s A f λ
Amplitude: total swing peak-to-peak = 2 A A = 1.2/2 = 0.6 m Kyun? Amplitude middle se measure hoti hai, poori swing ki aadhi.Frequency: f = 1/ T = 1/4 = 0.25 Hz Wavelength: λ = v / f = 3/0.25 = 12 m λ = v T = 3 × 4 = 12 m Kyun donon raaste agree karte hain? Kyunki v / f = v T 1/ f = T
Common mistake "Amplitude crest aur trough ke beech ki distance hai."Kyun sahi lagta hai: wave diagram par woh vertical distance sabse zyada visually obvious hoti hai, aur woh ek asli measurement bhi hai (peak-to-peak).
Fix: amplitude equilibrium line se peak tak measure hoti hai, isliye yeh crest-to-trough distance ki aadhi hoti hai: A = 2 1 ( peak-to-peak )
Common mistake "Agar mein frequency badhaaun, toh wave speed badh jaayegi."Kyun sahi lagta hai: zyada frequency lagti hai "zyada energetic / tez," aur tez hilane se wiggles tez baahir jaate hain... aisa lagta hai.
Fix: speed medium se set hoti hai (v = T / μ v f λ v
Common mistake "Wavelength aur period ek hi cheez hai."Kyun sahi lagta hai: dono "wave kitni baar repeat hoti hai" yeh batate hain, aur dono tab chhote hote hain jab frequency badhti hai.
Fix: λ space mein repeat hoti hai (metres), T time mein repeat hota hai (seconds). Alag dimensions hain! Yeh sirf speed ke through linked hain: λ = v T
Recall Quick self-test (answers chhupao)
Amplitude ko ek sentence mein define karo.
Speed ki definition se v = f λ
Agar v f λ
f T λ
Recall Feynman: ek 12-saal ke bacche ko samjhaoSoch ek lamba jump-rope hai. Amplitude hai ki tum rope ko floor ke upar kitna uchha uchhalte ho. Wavelength hai rope ke saath ek hump se agale hump tak ki distance. Period hai ki tum ek poora upar-neeche hila karne mein kitna time lete ho. Frequency hai ki tum har second mein kitni baar hilate ho. Aur speed hai ki ek hump kitni tez rope ke neeche tumhare dost ki taraf zoom karta hai. Kyunki har second mein tum f λ f × λ
Mnemonic Master equation yaad rakho"Very Fast Llamas" → V = F Λ f T f = 1/ T
Simple Harmonic Motion — har wave particle SHM karta hai; amplitude aur period seedha wahaan se aate hain.Transverse and Longitudinal Waves — yeh parameters dono wave types par laagu hote hain.Speed of Waves on a String — explain karta hai ki v = T / μ The Wave Equation y(x,t) — saare parameters combine karta hai: y = A sin ( k x − ω t ) k = 2 π / λ ω = 2 π f Doppler Effect — jab source/observer hilte hain toh f λ Sound Waves aur Electromagnetic Spectrum — v = f λ
Wave ka amplitude define karo Kisi particle ki equilibrium position se maximum displacement (peak-to-peak NAHIN; peak-to-peak = 2A).
Wavelength define karo Woh sabse chhoti distance jis par wave shape repeat hoti hai (jaise crest to crest), metres mein measure hoti hai.
Wave ka period define karo Ek particle ke ek poore oscillation ka time, seconds mein.
Frequency define karo Ek second mein poore oscillations ki sankhya, hertz mein measure hoti hai (Hz = s⁻¹).
f aur T mein relation f = 1/T (yeh reciprocals hain).
Fundamental wave equation batao v = fλ = λ/T.
v = fλ derive karo Ek period T mein ek crest ek wavelength λ aage badhti hai, isliye v = distance/time = λ/T = fλ.
Agar wave speed fix hai aur frequency double ho jaaye, toh wavelength ka kya hoga? Aadhi ho jaayegi, kyunki λ = v/f.
Wave ki speed kya determine karta hai? Medium ki properties (jaise string ke liye tension aur linear density), frequency nahin.
f, T, λ, v ke units f Hz mein, T seconds mein, λ metres mein, v m/s mein.
Ek wave ki f = 25 Hz, λ = 2 m hai. Speed? v = fλ = 25×2 = 50 m/s.
Wave repeats in space and time
