Class 12 Physics Notes | Waves & Thermodynamics

🌊 1. Wave Motion

A wave is a continuous transfer of disturbance from one part of a medium to another through successive vibrations of the particles of the medium about their mean positions.

The wave carries energy and transports momentum but not matter when it propagates in a medium.

📷 [PICTURE: A sinusoidal wave traveling left to right, arrows show energy transfer, particles stay in place] Fig: Progressive wave

📌 Mechanical Wave

The waves which require a material medium for their propagation are called mechanical waves.

📌 Transverse Wave

The wave in which the particles vibrate perpendicularly to the direction of propagation is called a transverse wave.

📷 [Transverse wave: particles up/down; crest, trough, wavelength λ] Crest & Trough

📌 Longitudinal Wave

The wave in which particles vibrate along the direction of propagation is called a longitudinal wave.

Examples sound wave in air, wave in a spring (compression & release), sea waves, seismic waves.

📷 [Longitudinal wave: compressions & rarefactions labeled, direction parallel to oscillation]

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📐 2. Important Wave Parameters

🔵 1. Wavelength (λ)
Distance between two nearest particles vibrating in same phase. Equals distance travelled during one complete vibration.

🔵 2. Frequency (f)
Number of waves/crests passing a point per second. f = 1/T (T = time period).

🔵 3. Time Period (T)
Time for one complete wave to pass a point.

🔵 4. Amplitude (a)
Maximum displacement from equilibrium position.

📷 [Sine wave with amplitude arrow and wavelength double arrow]

🔵 5. Wave Velocity (v)
Distance travelled by crest in one second.

v = λ / T = f λ

🔵 6. Phase
Position of wave relative to reference (measured in angles).

🔵 7. Particle Velocity (v_p)
Velocity of vibrating particles.

v_p = -v (dy/dx)

Particle velocity changes with time; wave velocity (v = fλ) is constant. Acceleration of wave = 0, particle acceleration ≠ 0.

📷 [Particle vertical motion vs horizontal wave motion]

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🎵 3. Standing Waves (Superposition)

When two waves of same frequency & amplitude travel in opposite directions → standing wave.

y = 2a cos(kx) sin(ωt)

Represents SHM with amplitude A = 2a cos(kx).

✨ Condition for Maximum Amplitude (Antinodes)

Maximum amplitude when |cos(kx)| = 1 → cos(2πx/λ) = cos(nπ)

x = nλ/2 (n = 0, 1, 2, …)

Antinodes occur at: x = 0, λ/2, λ, 3λ/2, … nλ/2

Phase difference φ = 0, π, 2π, …
Path difference = nλ/2

✅ Distance between two consecutive antinodes = λ/2

📷 [Standing wave pattern: nodes (zero displacement), antinodes (max displacement). distance λ/2 between nodes]

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🔥 4. Second Law of Thermodynamics

🔹 Kelvin-Planck Statement: It is impossible to design a device that works on a cycle and produces no other effect than heat transfer from a single body for the production of work.

📷 [Impossible engine: single reservoir → work, cross mark]

🔹 Clausius Statement: It is impossible for a self-acting machine working cyclically to transfer heat from a cold body to a hot body without external agency.

📷 [Heat flow cold→hot impossible without work, cross mark]

⚙️ 5. Heat Engine

Device converting heat energy into mechanical work. 3 parts: Source (hot body at T₁), Working substance, Sink (cold body at T₂).

📷 [Heat engine diagram: Source → Q₁, Engine → W, Sink → Q₂]

📈 Efficiency of Heat Engine

η = (Work done / Heat absorbed) × 100% = (W / Q₁) × 100%

W = Q₁ – Q₂ → η = (1 – Q₂/Q₁) × 100%

📷 [Energy flow: Q₁ input, W output, Q₂ rejected]

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🌀 6. Carnot Engine (Ideal Heat Engine)

Carnot engine has maximum efficiency; works on Carnot cycle consisting of two isothermal and two adiabatic processes.

📷 [Carnot engine sketch: Source T₁, Sink T₂, Working substance]

📌 Carnot Cycle Steps (P-V diagram)

a. Isothermal Expansion (A→B): Absorbs Q₁ at T₁ → W₁ = nRT₁ ln(V₂/V₁)
b. Adiabatic Expansion (B→C): Temperature drops T₁→T₂, W₂ = nR(T₁-T₂)/(γ-1)
c. Isothermal Compression (C→D): Rejects Q₂ to sink at T₂, W₃ = nRT₂ ln(V₃/V₄)
d. Adiabatic Compression (D→A): Temperature rises T₂→T₁, W₄ = nR(T₁-T₂)/(γ-1)

📷 [P-V diagram of Carnot cycle: AB isothermal exp, BC adiabatic, CD isothermal comp, DA adiabatic; area = net work]

Total work W = nRT₁ ln(V₂/V₁) − nRT₂ ln(V₃/V₄)

Net work = area enclosed by cycle ABCDA.

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📊 7. Efficiency of Carnot Cycle

η = [1 – (Q₂/Q₁)] × 100%

From isothermal processes: Q₁ = nRT₁ ln(V₂/V₁), Q₂ = nRT₂ ln(V₃/V₄)

η = [1 – (T₂ ln(V₃/V₄))/(T₁ ln(V₂/V₁))] × 100%

From adiabatic conditions: V₂/V₁ = V₃/V₄ → logarithms cancel.

✨ Carnot Efficiency (Ultimate equation):

η = 1 – (T₂ / T₁) (in fraction)

η = [1 – T₂/T₁] × 100%

📷 [Graph: Carnot efficiency vs temperature ratio, efficiency increases as T₁ increases or T₂ decreases]

❄️ 8. Refrigerator (Reverse Carnot Cycle)

Transfers heat Q₂ from cold body to hot body by doing external work W.

Coefficient of Performance (COP) = Q₂ / W = Q₂ / (Q₁ – Q₂)

Ideal refrigerator COP = T₂ / (T₁ – T₂)

📷 [Refrigerator schematic: Q₂ from cold reservoir, W input, Q₁ rejected to hot surroundings]

📷 [Real fridge: compressor, condenser coils, freezer compartment]

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📘 Key Formulae Summary — Wave velocity: v = fλ | Particle velocity: v_p = -v(dy/dx) | Carnot η = 1 – T₂/T₁ | Engine η = 1 – Q₂/Q₁

NEB Waves and wave motion Physics class 12 notes