Question bank — Mechanical waves — transverse and longitudinal

False. Har particle sirf apni rest spot ke aas-paas oscillate karta hai; jo travel karta hai woh pattern hai (aur uski energy/momentum), medium ka matter nahi.

False. Disturbance inter-particle forces (elasticity) aur mass (inertia) se aage jaati hai; particles nahi hain toh koi usse aage pass hi nahi kar sakta.

False. Air mein shear rigidity nahi hoti, isliye woh bulk mein sideways-vibration waves support nahi kar sakti — air mein sound purely longitudinal hoti hai.

True. Solid shear (→ transverse) aur compression (→ longitudinal) dono ko resist karta hai, isliye dono wave types usmein propagate hoti hain.

False. Non-dispersive medium mein $v$ medium se fix hota hai; $f$ badhane se sirf $\lambda$ chota hota hai taaki product constant rahe.

False. Woh curve pressure (ya displacement) versus position plot karta hai, sideways motion nahi — sound longitudinal hi rehti hai.

False. Crest par particle momentarily rest mein hota hai (SHM ka turning point); speed maximum hoti hai equilibrium line par, jahan $v_p=A\omega$ hota hai.

False. Kyunki $\lambda =v/f$ hai aur $v$ common hai, zyada frequency wali wave ki wavelength choti hogi.

False. $v\propto \sqrt{T}$ hai, isliye double tension se sirf $\sqrt{2}\approx 1.41$ ka factor badhta hai — square root ise tame kar deta hai. (Dekho Wave equation.)

False. Transverse wave mein particle velocity transverse (upar/neeche) hoti hai jabki wave velocity $x$ ke saath hoti hai; dono perpendicular hain, aur $v_p$ toh har half cycle mein sign bhi reverse karta hai.

Error: sound flying particles nahi hai. Air molecules sirf apne neighbours ko aage-peeche jostle karte hain; compression pattern travel karta hai, molecules local hi rehte hain. (Dekho Sound waves.)

Error: cork mostly ek chota closed loop trace karta hai aur wapas aata hai; sirf energy pool cross karti hai. Koi bhi tiny net drift ek second-order effect hai, wave khud nahi.

Error: loudness amplitude hai, frequency ya speed nahi; $v$ sirf medium par depend karta hai aur $\lambda$, $f$ ke hisaab se adjust hota hai, kabhi amplitude ke hisaab se nahi.

Error: $A\omega$ maximum particle speed hai, jo ek upar-neeche ki quantity hai. Wave (pattern) speed hai $v=\omega /k=f\lambda$ — yeh alag formula aur alag meaning hai.

Error: $+kx$ sign ka matlab hai ki phase tab constant hota hai jab $t$ badhne par $x$ ghatता hai, isliye yeh wave $-x$ direction mein travel karti hai. $+x$ mein move karne wali wave $\sin (\omega t-kx)$ hoti hai.

Error: minus sign ek delay hai: $x$ par particle woh ab karta hai jo source ne $x/v$ time pehle kiya tha, isliye woh lag karta hai, lead nahi.

Error: yahan density inertia hai, jo denominator mein hai: $v=\sqrt{T/\mu }$, isliye zyada mass-per-length $\mu$ wave ko slower banata hai, faster nahi.

Neighbour ko sideways kheenchne ke liye aapko ek force chahiye jo shape change (shear) ko oppose kare; usse line ke saath kheenchne ke liye sirf squeeze hone ki resistance chahiye, jo har gas/liquid/solid mein hoti hai.

Medium $v$ fix karta hai, aur $v=f\lambda$ hold karna chahiye, isliye agar $f$ badhta hai toh $\lambda =v/f$ ko $v$ constant rakhne ke liye girna padta hai.

Zyada restoring force particles ko tezi se wapas snap karta hai (numerator) jabki zyada inertia unhe sluggish banata hai (denominator); square-root form wahi nikalta hai jo medium element par Newton's law $F=ma$ se aata hai. (Dekho Wave equation.)

Har particle sirf apne neighbour ki motion thodi der baad copy karta hai, isliye shape aage badhti hai even though koi particle apna neighbourhood nahi chhodta — stadium ka "Mexican wave" idea.

$y=A\sin (\omega t-kx)$ ke dono derivatives same cosine share karte hain, aur unka ratio $\omega /k=v$ hai; minus sign kehta hai ki curve ke rising-to-the-right part par particle neeche move kar raha hai jab wave aage slide karti hai.

$\lambda =v/f$; same $f$ sirf tab same $\lambda$ deta hai jab $v$ same ho, aur $v$ medium ki stiffness aur density ke saath badalta hai.

Woh bulk mein propagate nahi kar sakti — fluid mein shear rigidity nahi hoti, isliye sirf longitudinal (sound) waves interior mein survive karti hain. (Surface water waves ek special mixed case hain, bulk transverse nahi.)

Koi meaningful disturbance nahi bachti: $y\to 0$ har jagah, isliye transport karne ke liye koi energy nahi hai even though $\omega$, $k$, $v$ abhi bhi defined hain.

$v=\sqrt{T/\mu }\to 0$ — koi restoring force nahi hai toh disturbance aage pass nahi ho sakta, isliye koi wave travel nahi karti.

Haan — har travelling wave apna $v=f\lambda$ maintain karti hai; unka sum ek standing pattern banata hai, lekin woh superposition kisi bhi wave ki speed nahi badalta. (Dekho Standing waves & resonance aur Superposition and Interference.)

Speed maximum hai ($A\omega$) aur acceleration zero hai, kyunki restoring force $\propto -y$ hai jo $y=0$ par vanish ho jaati hai — SHM ki pehchaan. (Dekho Simple Harmonic Motion.)

Nahi — $v$ air se fix hota hai; observed frequency shift hoti hai (Doppler) jabki medium mein wave speed same rehti hai. (Dekho Doppler effect.)

Frequency source se set hoti hai aur continuous rehti hai, lekin $v$ drop hota hai (zyada $\mu$) isliye $\lambda =v/f$ heavier string mein chota ho jaata hai.