1.6.14 · D1Wave parameters — amplitude, wavelength, frequency, period,
Ek wave ek aisi wiggle hai jo space mein repeat hoti hai (tum dekh sakte ho ki ek hi shape har itne metres mein milti hai) aur time mein bhi (ek jagah ek steady beat par hiltii rehti hai). Parent page par jo bhi symbol hai, woh bas usi repeat ka naam hai — kitni badi hai, kitni lambi hai, kitni baar hoti hai, ya kitni tezi se chalti hai.
Pehle v = f λ sach mein samajhne se pehle — tumhe ye jaanna chahiye ki har squiggle ka matlab kya hai aur — aur isse bhi zaroori — ek real wave par woh kaisa dikhta hai . Yeh page har symbol ko bilkul zero se banata hai. Hum dheere chalenge, ek picture at a time. Yahan kuch bhi assume nahi kiya gaya; jo bhi parent note mein use hua hai, usse hum neeche define karenge.
Waves ke baare mein sabse mushkil baat yeh hai ki ek hi picture ke peeche do alag graphs hote hain, aur beginners unhe mix kar dete hain. Aao inhe abhi se saaf alag kar lete hain.
Definition Wave ko dekhne ke do tarike
Ek snapshot time ko rok deta hai aur medium ke saath dekhta hai: horizontal axis position x (metres) hoti hai. Yeh wahi hai jo ek rope ki photograph mein dikhta hai.
Ek ek particle ki movie EK jagah chunti hai aur usse time ke saath dekhti hai: horizontal axis time t (seconds) hoti hai. Yeh wahi hai jo paani par ek cork trace karta hai.
Dono paper par bilkul ek jaise dikh sakte hain — ek wavy curve — lekin horizontal axis ka matlab bilkul alag hota hai. Wavelength snapshot par hoti hai; period movie par hoti hai.
Yeh split apne dimaag mein rakho. Aadha wave confusion to bas yahi hai ki koi "space" ki length ko "time" graph se padh leta hai ya ulta.
y y itna hai ki ek particle apni rest position se abhi kitna door hai , abhi ke waqt measure kiya gaya. Upar positive y y
Picture: snapshot mein, curve ki height beech ki flat line ke upar y y = 0
y y y = 0 y
Equilibrium line woh flat level hai jis par medium tab rest karta hai jab koi wave nahi hoti — calm-water level, slack rope. Har graph par yeh woh horizontal centre line hai jahan y = 0
Picture: neeche wali figure mein dashed beech wali line. Crests uske upar niklte hain; troughs uske neeche dip karte hain.
Common mistake "Wave ka bottom zero hai."Kyun sahi lagta hai: trough sabse neeche wala point hai jo dikhayi deta hai, toh woh floor jaisa lagta hai.
Fix: zero beech mein hai, neeche nahi. Trough y = − A neeche jitna crest upar hota hai). Yahi woh galti ki jad hai jo parent note mein classic amplitude error ke baare mein batata hai.
Definition Crest, trough, amplitude
Crest wave ka sabse ucha point hai (maximum y Trough sabse neecha point hai (minimum y Amplitude A woh doori hai jo equilibrium line se crest tak hai (equivalently, trough tak ). Units: metres.
Picture: figure mein, beech ki line se crest ki tip tak ka magenta arrow A peak-to-peak hai, jo 2 A
Intuition "Beech se" kyun, naa ki "top to bottom"Ek particle equilibrium ke baare mein symmetrically oscillate karta hai: woh utna hi upar jaata hai jitna neeche. Us motion ka natural size ek taraf ka swing hai, A ∝ A 2
λ λ medium ke saath sabse kam doori hai jiske baad shape repeat hoti hai . Crest se agle crest tak, ya trough se agle trough tak. Units: metres. Yeh ek snapshot quantity hai.
Picture: snapshot (position axis) par, λ
sabse chhota repeat measure karte hain
Shape 2 λ 3 λ fundamental repeat distance hai, sabse chhoti brick jisse poora pattern tila gaya hai.
T T time hai jisme ek single particle ka ek full up-and-down cycle pura hota hai . Units: seconds. Yeh ek movie quantity hai — isse dekhne ke liye ek jagah ko time ke saath watch karna padta hai.
Picture: movie graph (time axis) par, T time-axis twin hai.
T λ λ space mein repeat hai (metres) aur T time mein repeat hai (seconds). Bilkul alag dimensions. Yeh dono sirf wave ki speed ke zariye milte hain, jo hum D-later pages mein banate hain: λ = v T
f f woh number hai jitne complete cycles ek particle har second mein complete karta hai . Units: hertz, jahan 1 Hz = 1 s − 1
f = 1/ T T = 0.25 s divide karte ho: 1 ÷ 0.25 = 4 f = 1/ T
v v fixed phase ka ek feature (jaise, ek particular crest) medium se guzarta hai. Units: metres per second, m/s ÷
Picture: do snapshots compare karo jo thodi si alag time par li gayi hain — poora pattern sideways khisakal gaya hai. Ek crest track karo; woh kitna move hua divided by kitna time laga woh v
v medium decide karta hai (rope ki tension aur weight, air ki stiffness). Zyada tezi se shake karne se zyada crests ban jaate hain, zyada paas pack hue — iska matlab yeh nahi ki har ek zyada tezi se travel karta hai. Isliye baad mein f λ v
Definition Symbols ko zor se padhna
λ length in space (wavelength) ke liye use hota hai.T period (ek time). Yahan temperature nahi!f frequency .Hz hertz , frequency ki unit, = s − 1 s − 1 − 1 s − 1 = 1/ s ≡ defined as" ("equals" se zyada strong: yeh meaning set karta hai).∝
− 1 s − 1 v = f λ [ s − 1 ] × [ m ] = m/s tumhare liye bookkeeping karta hai .
Displacement y and equilibrium y=0
Wavelength lambda in space
Wave equation v = f lambda
Top-down padho: displacement aur equilibrium amplitude define karte hain; space-repeat se wavelength milti hai, time-repeat se period milti hai; period flip hokar frequency ban jaata hai; wavelength aur period milkar speed set karte hain; aur frequency times wavelength tumhe woh master equation deta hai jis par pura topic built hai.
Right-hand side cover karo aur dekho ki reveal karne se pehle answer de sako ya nahi.
y Ek particle abhi apni rest position se kitna door hai, metres mein (upar positive, neeche negative).
Wave par y = 0 Equilibrium line par — flat beech mein, trough mein nahi.
Amplitude A Equilibrium line se crest tak ki doori; peak-to-peak swing ka aadha.
A 2 A
Wavelength λ Sabse kam doori jis par shape repeat hoti hai (crest to crest); metres mein ek space quantity.
Period T Ek particle ka ek full cycle ka time; seconds mein ek time quantity.
f = 1/ T "Cycles per second" total time (1 s) divided by time-for-one-cycle (T 1/ T
1 Hz Ek complete cycle per second, yani s − 1
Wave speed v Medium ki properties, naa ki tum kitni tezi se shake karte ho.
s − 1 "Per second"; − 1 v = f λ
Simple Harmonic Motion — yahan har particle ki up-and-down motion hi SHM hai; A T Transverse and Longitudinal Waves — yahi symbols dono wave types describe karte hain.The Wave Equation y(x,t) — in sab symbols ko y = A sin ( k x − ω t ) Speed of Waves on a String — explain karta hai ki v 
