🔬 Unit 2 – Part A (2-Mark Q&A)

1) Torsional pendulum

A rigid body (disc/rod) suspended by a thin wire. Small twist → restoring torque by wire → angular SHM.

τ = −C θ (C: torsion constant), I d²θ/dt² + C θ = 0, period T = 2π√(I/C).

2) Travelling vs Standing waves (energy)

• Travelling: Net energy transport along propagation.
• Standing: No net transport; energy oscillates within loops between nodes/antinodes.

Standing wave formed by superposition of two opposite travelling waves of same f, A.

3) Weber–Fechner law

Perceived sensation is proportional to log of stimulus intensity:

S = k log(I/I₀) (I₀: threshold).

4) Doppler effect (sound)

Apparent frequency changes due to relative motion of source/observer.

f' = f \frac{v \pm v_o}{v \mp v_s} (signs: approach ↑, recede ↓); v is speed of sound.

5) Four sound-absorbing materials

• Acoustic foam / mineral wool
• Fiberglass panels
• Heavy curtains
• Cork / perforated boards

6) Classification by frequency

• Infrasound: f < 20 Hz
• Audible: 20 Hz – 20 kHz
• Ultrasound: f > 20 kHz

7) Properties of ultrasonics

• Very high f, short λ → less diffraction, good directionality
• Reflect, refract, absorb; cause heating & cavitation in liquids
• Penetrate solids/liquids → NDT, imaging

8) Magnetostriction & ultrasound production

Ferromagnets (Ni/Fe/Co) change length in a magnetic field. A rod in a coil with high-frequency AC experiences rapid elongation/contraction → emits ultrasonic waves.

Resonance when drive f matches rod’s natural longitudinal mode.

9) Three applications of ultrasonics

• Medical imaging: Sonography
• NDT: Flaw/thickness detection
• SONAR: Range/depth mapping
• Plus: Ultrasonic cleaning, nebulizers

10) Bimetallic strip & use

Two bonded metals with different thermal expansion. Heating bends strip toward lower-expansion metal.

Used in thermostats, circuit breakers, dial thermometers.

11) Coefficient of thermal conductivity (k)

Rate of heat flow per unit area for unit temperature gradient (normal to area).

Q̇ = −k A (dT/dx); SI unit: W m⁻¹ K⁻¹.

12) Why roofs are painted white in summer?

White has high reflectance & low absorptance → less solar heat gain → cooler building & reduced AC load.

13) Thermal behavior of Invar

Fe–Ni alloy (~64% Fe, ~36% Ni) with very low CTE near room temperature → minimal expansion; used in precision instruments, clock pendulums, gauge blocks.

14) Seebeck effect

Temperature difference between junctions of two dissimilar conductors produces an EMF → continuous current in closed circuit. Basis of thermocouples.

Seebeck coefficient: S = ΔV/ΔT.

15) Heat conducted through a slab (numerical)

Given: A = 90×10⁻⁴ m², d = 1.2×10⁻³ m, ΔT = 20 K, k = 0.04 W m⁻¹ K⁻¹, Δt = 1 s.

Fourier: Q = kA(ΔT/d)Δt = 0.04×0.009×(20/1.2×10⁻³)×1 = 6 J.