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Question
At what temperature will the speed of sound be double of its value at 0°C?
Solution
Let the speed of sound T1 be v1,
where T1 = 0˚ C = 273 K.
Let T2 be the temperature at which the speed of sound (v2) will be double its value at 0˚ C.
As per the question,
v2 = 2v1.
\[v \propto \sqrt{T}\]
∴
\[\frac{{v_2}^2}{{v_1}^2} = \frac{T_2}{T_1}\]
\[ \Rightarrow \frac{\left( 2 v_1 \right)^2}{{v_1}^2} = \frac{T_2}{273}\]
\[ \Rightarrow T_2 = 273 \times 4 = 1092 K\]
To convert Kelvin into degree celsius:
\[T_2 = \left( 273 \times 4 \right) - 273 = 819^\circ C\]
Hence, the temperature (T2 ) will be 819˚ C
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