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Question
At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?
Solution
We know that `v ∝ sqrt(T)`
⇒ `v_T/v_0 = sqrt(T/T_0)`
Given that, `v_T = 3v_0`
∴ `(3v_0)/v_0 = sqrt(T/(273 + 0))`
⇒ `sqrt(T) = 3sqrt(273)`
⇒ T = 9 × 273
⇒ T = 2457 K
⇒ T = 2457 – 273
⇒ T = 2184°C
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