Sound Waves

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1. **Amplitude (A)**: Maximum displacement from equilibrium position 2. **Wavelength (λ)**: Distance between two consecutive points in phase (crest to crest) 3. **Frequency (f)**: Number of complete o

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**Transverse Waves:** - Particle oscillation ⊥ to wave propagation - Has crests and troughs - Examples: Water waves, light waves **Longitudinal Waves:** - Particle oscillation ∥ to wave propagation -

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**y(x,t) = A sin(kx ± ωt + φ)** Where: - y(x,t) = displacement at position x and time t - A = amplitude - k = wave number = 2π/λ - ω = angular frequency = 2πf - φ = phase constant - ± sign: (-) for r

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**Formula: v = √(E/ρ)** Where: - E = elastic modulus of medium - ρ = density of medium **In air at 20°C:** v ≈ 343 m/s **Note**: Speed increases with temperature in gases, and is much higher in sol

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**Principle**: When two or more waves pass through the same medium, the resultant displacement is the algebraic sum of individual displacements. **Example**: Wave 1: y₁ = A sin(kx - ωt) Wave 2: y₂ =

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**Fixed Boundary (e.g., closed end of pipe):** - Wave reflects with 180° phase change - Incident and reflected waves are out of phase - Forms a node at the boundary **Free Boundary (e.g., open end of

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**Closed Pipe**: One end closed, one end open **Boundary conditions**: - Node at closed end - Antinode at open end **For fundamental mode**: Length l = λ₁/4 Therefore: λ₁ = 4l **Fundamental frequen

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**Open Pipe**: Both ends open **Boundary conditions**: - Antinodes at both ends - Node in between **For fundamental mode**: Length l = λ₁/2 Therefore: λ₁ = 2l **Fundamental frequency**: f₁ = v/λ₁ =