The velocity of sound in air is doubled when the temperature is raised from 0°C to α°C. The value of α i s _______.

Question

G1 Physics · Accepted Answer

For a gas, v ∝ √T, where T is absolute temperature. Initially, T₁ = 273 K. The final speed is twice the initial speed: v₂ = 2v₁. Therefore, v₂/v₁ = √(T₂/T₁). Hence, 2 = √(T₂/273). Squaring, 4 = T₂/273. Thus, T₂ = 4×273 = 1092 K. If the final Celsius temperature is α°C, T₂ = α+273. Therefore, α+273 = 1092. Hence, α = 819°C. Therefore the answer is 819.