Speed of Sound (Newton-Laplace) (v = √(B/ρ) = √(γP/ρ) for ideal gas)
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v = √(B/ρ) = √(γP/ρ) for ideal gas
What each symbol means
| Symbol | What it stands for |
|---|---|
| B | Bulk modulus of the medium (Pa) |
| P | Pressure of gas (Pa) |
| v | Speed of longitudinal wave / sound (m/s) |
| γ | Ratio of specific heats Cp/Cv (dimensionless) |
| ρ | Density of the medium (kg/m³) |
When to use this
General formula: v = √(B/ρ) for any medium. For ideal gas: B_adiabatic = γP (Laplace correction). Newton's original formula v = √(P/ρ) gave 280 m/s (15% low). Laplace corrected to √(γP/ρ) giving 331 m/s. For solids: v = √(Y/ρ) using Young's modulus. v ∝ √T for ideal gas (since P/ρ ∝ T). NCERT Eqs. 14.19, 14.24.