gen-define-the-speed-of-sound-in-a-medium-and-give-one-short-wor-33c4

Define the speed of sound in a medium and give one short worked example.

# Speed of Sound in a Medium ## Definition The **speed of sound** in a medium is the distance traveled per unit time by a sound wave as it propagates through an elastic material. It depends on the medium's physical properties: **For gases:** $$v = \sqrt{\frac{\gamma RT}{M}}$$ **For solids:** $$v = \sqrt{\frac{E}{\rho}}$$ **For liquids:** $$v = \sqrt{\frac{K}{\rho}}$$ where: - γ = adiabatic index - R = gas constant - T = absolute temperature - M = molar mass - E = Young's modulus - K = bulk modulus - ρ = density --- ## Worked Example **Problem:** Calculate the speed of sound in air at 20°C, given that at 0°C it is 331 m/s. **Solution:** The speed of sound in air varies with temperature as: $$v = v_0\sqrt{\frac{T}{T_0}}$$ Or approximately: $v = 331 + 0.6T$ (where T is in °C) Using the simpler formula: $$v = 331 + 0.6(20)$$ $$v = 331 + 12$$ $$v = 343 \text{ m/s}$$ **Answer:** The speed of sound in air at 20°C is **343 m/s**.