At what temperature does the velocity of soun | vedclass

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(B) The speed of sound in air is directly proportional to the square root of the absolute temperature ($T$ in Kelvin).Mathematically,$v \propto \sqrt{

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$57$

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(B) The speed of sound in air is directly proportional to the square root of the absolute temperature ($T$ in Kelvin).Mathematically,$v \propto \sqrt{T}$.Let $v_1$ be the velocity at $T_1 = 0^{\circ}C = 273 \ K$.Let $v_2$ be the velocity at temperature $T_2$.Given that the velocity increases by $10\%$,we have $v_2 = v_1 + 0.10v_1 = 1.1v_1 = \frac{11}{10}v_1$.Using the ratio formula: $\frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}}$.Substituting the values: $\frac{v_1}{1.1v_1} = \sqrt{\frac{273}{T_2}}$.$\frac{1}{1.1} = \sqrt{\frac{273}{T_2}} \Rightarrow \frac{1}{1.21} = \frac{273}{T_2}$.$T_2 = 273 	imes 1.21 = 330.33 \ K$.Converting back to Celsius: $T_2(^{\circ}C) = 330.33 - 273 = 57.33^{\circ}C \approx 57^{\circ}C$.

At what temperature does the velocity of sound in air increase by $10\%$ compared to its velocity at $0^{\circ}C$ (in $^{\circ}C$)?

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