The speed of sound in an ideal gas is 330 m/s at 300 K. At another temperature the speed becomes 363 m/s. Assuming γ is unchanged, if the new temperature is N K, find N.
Physics · Wave Motion · sound wave
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Question

The speed of sound in an ideal gas is 330 m/s at 300 K. At another temperature the speed becomes 363 m/s. Assuming γ is unchanged, if the new temperature is N K, find N.

G1 Physics · Accepted Answer

For the same gas, v ∝ √T. Therefore, v₂/v₁ = √(T₂/T₁). Hence, T₂ = T₁(v₂/v₁)². Substitute: T₂ = 300(363/330)² = 300(1.1)² = 300(1.21) = 363 K. Hence, N = 363.