Sound

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A mechanical wave is a wave that requires a material medium for its propagation. The disturbance travels through the medium without causing any flow of material, but transfers energy and momentum. Ex

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v = nλ Where: • v = velocity of wave (m/s) • n = frequency (Hz or s⁻¹) • λ = wavelength (m) This equation shows that wave velocity is constant in a given medium. If frequency increases, wavelength d

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**Transverse Waves:** • Particles vibrate perpendicular to wave propagation • Have crests and troughs • Can be polarized • Example: Water waves, EM waves **Longitudinal Waves:** • Particles vibrate p

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**Amplitude (A):** Maximum displacement of particles from equilibrium position (measured in meters) **Wavelength (λ):** Distance between two successive particles in same phase OR distance covered by

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**Newton's Formula:** v = √(P/ρ) Where: • P = atmospheric pressure • ρ = density of air **Calculation at NTP:** P = hdg = 0.76 × 13600 × 9.8 = 101,293 Pa ρ = 1.293 kg/m³ v = √(101,293/1.293) = √78,

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**Laplace's Correction:** v = √(γP/ρ) Where γ = Cp/Cv = 1.41 for air (adiabatic ratio) **Reasoning:** Sound propagation is adiabatic (rapid process) not isothermal as Newton assumed. **Calculation

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**Derivation:** From ideal gas law: v = √(γRT/M) At temperatures T₀ and T: v₀ = √(γRT₀/M) and v = √(γRT/M) ∴ v/v₀ = √(T/T₀) **For small temperature changes:** v = v₀ + 0.61t (where t is in °C) **K

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**Given:** • Distance to wall = 60 m • Velocity of sound = 330 m/s • Find: Time to hear echo **Solution:** Total distance travelled by sound = 2 × 60 = 120 m (Sound travels to wall and back) Time =