PhysicsWaves

Effective Study Strategies

• Understand wave classification: Mechanical vs EM waves, transverse vs longitudinal, progressive vs stationary.
• Master the wave equation: v = fλ. Know that frequency remains constant when wave changes medium, but velocity and wavelength change.
• Sound speed calculations: v = √(E/ρ) where E = modulus of elasticity. For gases: v = √(γP/ρ) = √(γRT/M).
• Superposition principle: Net displacement = vector sum of individual displacements. Leads to interference, beats, standing waves.
• Interference conditions: Constructive: path difference = nλ. Destructive: path difference = (n+½)λ.
• Beats formula: Beat frequency = |f₁ – f₂|. Used for tuning musical instruments.
• Standing waves: Formed by interference of identical waves traveling in opposite directions. Nodes (zero amplitude) and antinodes (max amplitude).
• Doppler effect formulas: Memorize all 4 cases (source/observer moving toward/away). f’ = f(v ± v₀)/(v ∓ vₛ).

Exam Preparation Tips

• Memorize key formulas on flashcards: v = fλ, v = √(T/μ) for strings, beat frequency = |f₁ – f₂|, Doppler formulas.
• Practice standing wave patterns: Strings fixed at both ends: L = nλ/2. Pipes: open-open: L = nλ/2, open-closed: L = (2n-1)λ/4.
• Solve speed of sound problems: v ∝ √T (absolute temperature). v increases by ~0.6 m/s per °C rise.
• Understand Laplace correction: Sound propagation in gases is adiabatic, not isothermal. γ = Cₚ/Cᵥ = 1.4 for air.
• Doppler effect sign conventions: Numerator: + when observer moves toward source, – when away. Denominator: – when source moves toward observer, + when away.
• Time yourself on complex problems: Set a timer for 3-4 minutes per problem to simulate exam conditions.

Common Pitfalls to Avoid

• Confusing transverse (particles vibrate ⊥ to propagation) with longitudinal (particles vibrate ∥ to propagation)
• Forgetting that frequency doesn’t change when wave enters new medium (only v and λ change)
• Mixing up nodes and antinodes in standing waves: Nodes = zero displacement, Antinodes = max displacement
• Using wrong harmonic formulas for pipes: Open-closed pipe has only odd harmonics (f, 3f, 5f…)
• Wrong sign convention in Doppler effect formulas
• Assuming sound speed depends on pressure (it doesn’t at constant temperature – v ∝ √T only)
• Confusing beat frequency with average frequency: Beats = |f₁ – f₂|, not (f₁ + f₂)/2
• Forgetting that EM waves don’t need medium, mechanical waves do
• Not converting units properly (cm to m, °C to K, etc.)