1.6.3 · D5 · HinglishOscillations & Waves
Question bank — ω, T, f relationships
1.6.3 · D5· Physics › Oscillations & Waves › ω, T, f relationships
Shuru karne se pehle, teen plain-word anchors (kabhi assume mat karo):
- Cycle = motion ka ek complete repeat — wapas usi position par usi direction mein chalte hue.
- Radian = angle naapne ka ek tarika jahan ek poora chakkar radians ke barabar hota hai (approximately ). Ye ek pure number hai, metre jaisi "real" unit nahi.
- Phase = mein cosine ke andar baitha angle — ye batata hai ki tum cycle mein kahan ho.
Do tasveerein poore page ko anchor karti hain. Jab tum traps solve karo tab inhe saamne rakho.
Upar wala triangle teen quantities ko corners ke roop mein dikhata hai jo apne conversions se jude hain — sirf un do edges par rehta hai jo ko touch karti hain. Neeche wali circle picture dikhati hai kyun: ek oscillation ek point ke circle mein ghoomne ki shadow hoti hai, isliye ek lap ( rad) ek cycle ke barabar hota hai.
True or false — justify
A doubling of frequency doubles the angular frequency .
True — kyunki ek seedhi proportionality hai (slope ke saath origin se guzarne wali line), ko scale karne par bhi usi factor se scale hota hai; ek fixed conversion constant hai jo kabhi nahi badlta, isliye ye doubling ko distort nahi kar sakta.
A doubling of frequency doubles the period .
False — inverse hai, isliye double karne par aadha ho jaata hai. Physically: agar tum har second mein do gune cycles thoons rahe ho, toh har individual cycle ko aadha waqt mein khatam hona padega.
and have the same units.
False — cycles per second (Hz) mein hai, radians per second mein. Ye sirf isliye ek jaisi lagti hain kyunki radian dimensionless hai (ek pure ratio), lekin "cycles" vs "radians" ka physical content ek cycle mein theek radians se alag hota hai.
Period and frequency are reciprocals of each other.
True — ek cycle seconds leti hai, isliye ek second mein cycles fit hoti hain, aur wahi count hi hai; isliye . Dono ek hi baat ko ulte direction mein padh rahe hain (seconds-per-cycle vs cycles-per-second).
A larger angular frequency always means a shorter period.
True — , isliye bada (tezi se angle sweep karna) matlab radians ka fixed target jaldi pura ho jaata hai, aur chhota milta hai. Ye strict inverse hai, isliye statement har positive ke liye sahi hai.
Two oscillators with the same must have the same .
True — sirf par depend karta hai (amplitude, mass, ya phase kuch bhi enter nahi karta), isliye equal periods se equal angular frequencies force hoti hain. Amplitude aur phase freely alag ho sakte hain aur kuch nahi badlta.
Changing the amplitude changes the frequency of an SHM.
False — ideal SHM mein kabhi mein enter nahi karta. Spring ke liye, (stiffness aur mass ke saath): restoring force displacement ke proportion mein badhti hai, isliye bada swing proportionally bada pull-back feel karta hai aur extra distance usi waqt mein cover ho jaati hai — rhythm untouched rehti hai. Dekho Springs and Pendulums.
The frequency in Hz equals the number of radians swept per second.
False — Hz cycles per second count karta hai; radians swept per second hai, jo usi motion ke liye guna bada hota hai kyunki har cycle radians worth ki hoti hai.
A negative angular frequency is physically meaningless.
False — par sign sirf reference circle ke rotation ki direction encode karta hai (clockwise vs anticlockwise). Kyunki , observed SHM position identical hoti hai, isliye hum conventionally lete hain aur koi bhi direction phase mein absorb kar lete hain; ye ek choice hai, koi law nahi.
Spot the error
Error: ", since the connects period and frequency."
Wrong pairing — ki units seconds hain, isliye ye reciprocal hona chahiye . sirf (radians) ke saath belong karta hai, jisse milta hai; triangle figure dekho — kabhi edge par nahi baithta.
Error: "."
galat jagah hai: (multiply) ya equivalently (period se divide, frequency se nahi). Units check karo — rad/s (rad) (cycles/s), isliye ye ke saath ek product hona chahiye.
Error: "In , the frequency is Hz."
hai (rad/s mein ka coefficient), nahi. Frequency Hz hai. Saamne ka number amplitude hai, rhythm se uska koi lena-dena nahi.
Error: "Since is 'angular frequency', I'll set my calculator to degrees when evaluating ."
Phase radians mein hai, degrees mein nahi — degree mode bilkul galat SHM curve deta hai. Oscillations ke liye calculator radian mode mein rakho.
Error: " because both describe how fast the oscillation is."
Dono speed ke saath badhte hain lekin equal nahi hain — radians/s count karta hai aur cycles/s, aur ek cycle radians hai, isliye .
Error: "A wave with higher frequency has a longer wavelength at fixed speed."
Ulta hai — Wave Speed v = fλ se, fixed par wavelength se inversely related hai, isliye higher frequency ka matlab shorter wavelength hai.
Error: "."
Multiply nahi, divide karo: . Tum radians/s ko cycles/s mein convert kar rahe ho, isliye radians-per-cycle ko strip out karte ho, ek aur add nahi karte.
Error: "A negative frequency means the oscillator has negative energy."
Nahi — (ya ) par sign flip reference circle ke rotation ke sense ko reverse karta hai, energy ko nahi; energy amplitude aur par depend karti hai, dono sign se unaffected hain. Physically hum rakhte hain aur direction mein daal dete hain.
Why questions
Why does the factor appear in and nowhere in ?
Kyunki "angle per cycle" hai — ye sirf tab enter karta hai jab tum cycles ko radians mein translate karte ho. aur dono cycles/seconds mein baat karte hain, isliye unke beech koi angle conversion zaroori nahi. Triangle figure mein, theek un do edges par dika hota hai jo par milti hain.
Why is angular frequency measured in radians per second rather than degrees per second?
Kyunki SHM Uniform Circular Motion ko project karne se aata hai, aur radians circle ke poore turn ko exactly banate hain, jo cosine ke liye natural argument hai aur ko clean rakhta hai (degrees ugly factors force karenge).
Why do we say oscillation is "the shadow of circular motion"?
Ek point circle ke around steadily ghoomte hua, edge-on dekha jaaye toh exactly SHM jaisi aage-peechhe movement karta hai (circle figure dekho — axis par projection trace karta hai); ek lap ( rad) ek oscillation cycle ke barabar hai, aur yahi reason hai ki (ek rotation rate) back-and-forth motion govern karta hai. Dekho Uniform Circular Motion.
Why is the quantity that sits inside the cosine, not or ?
Cosine ka input radians mein ek angle hona chahiye, aur exactly wahi deta hai (rad/s × s = rad). ya andar use karna galat argument deta jab tak rebuild na karo.
Why can we talk about the same oscillation with three different numbers (, , ) without contradiction?
Ye same rhythm ko alag "currencies" mein describe karte hain — seconds-per-cycle, cycles-per-second, aur radians-per-second — fixed conversions se jude (, ), isliye ye hamesha agree karte hain.
Why does the phase advance by exactly over one period?
Ek period by definition ek full cycle hoti hai, aur ek full cycle poore circle ko sweep karne ke barabar hai, jo radians hai — isliye , jo se match karta hai. Dekho Phase and Phase Difference.
Why does a stiffer spring (larger ) oscillate faster?
Kyunki (stiffness over mass ): bada spring constant matlab usi displacement ke liye zyada strong restoring pull, isliye mass jaldi wapas khinchta hai, aur isliye badh jaata hai jabki ghatta hai. Dekho Springs and Pendulums.
Why does a longer pendulum swing more slowly?
Kyunki (gravity over length ): bada length ratio ko ghataata hai, kam ho jaata hai, isliye period ke saath badhta hai. Rhythm geometry aur gravity se set hoti hai, kabhi swing ke size se nahi. Dekho Springs and Pendulums.
Edge cases
What is the period of something that never repeats (e.g. a mass that just sits still)?
Koi finite period nahi hai — , aur infinity tak blow up kar jaata hai, matlab "ek cycle hone mein hamesha ka waqt lagta hai." Ek non-oscillating object ki frequency zero hoti hai.
As , what happens to ?
— angle itna dheere sweep hota hai ki ek full cycle unboundedly lamba waqt leta hai, yaani motion effectively repeat karna band kar deti hai.
As , what happens to and ?
Dono apni limits tak jaate hain: (infinitely brief cycles) aur (infinitely many cycles per second).
Can the period be zero for a real oscillation?
Nahi — zero period ke liye infinite frequency chahiye hogi (infinitely fast repeats), jo physically impossible hai; genuine motion ke liye hamesha.
Is the same physical situation as ?
Haan — kyunki , ek zero hota hai theek tabhi jab doosra bhi hota hai, aur dono "no oscillation" describe karte hain (koi cycles nahi, koi angle sweep nahi).
What does flipping the sign of do to the motion ?
Kuch visible nahi hota — kyunki ek even function hai, , isliye position graph identical hai; sign sirf record karta hai ki imagined reference point clockwise ghoomta hai ya anticlockwise, jise hum usually phase mein dafna dete hain.
If two SHMs have identical but different phase , do they have the same period?
Haan — period sirf par depend karti hai (); sirf shift karta hai ki har kahan se cycle mein start karta hai, ye nahi ki ek cycle kitni lamba hai. Dekho Phase and Phase Difference.
A pendulum on the Moon swings more slowly than on Earth. Does its increase or decrease?
increase hota hai — kamzor gravity se chhota milta hai, aur badhta hai jab ghatta hai. Dekho Springs and Pendulums.
Connections
- ω, T, f relationships — parent note jise ye traps stress-test karte hain.
- Simple Harmonic Motion — jahan cosine ke andar rehta hai.
- Uniform Circular Motion — aur ka origin.
- Phase and Phase Difference — phase kaafi items mein probe ki gayi hai.
- Wave Speed v = fλ — frequency–wavelength trap.
- Springs and Pendulums — amplitude-independence aur gravity edge cases.