At what temperature will the speed of sound be double of its value at $0 ° C$ ?

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Solution

Step 1. Given data :
$T_{1} = 273 K$
Speed $(V)$ ,
$V_{2} = 2 V_{1}$ ,
$T_{2} = ?$
Step 2. Find the temperature :
$V α \sqrt{T}$
$V^{2} = T$
$\frac{T_{1}}{T_{2}} = \frac{{V_{2}}^{2}}{{V_{1}}^{2}} T_{2} = \frac{{V_{2}}^{2}}{{V_{1}}^{2}} \times T_{1} T_{2} = \frac{4 {V_{1}}^{2}}{{V_{1}}^{2}} \times T_{1} T_{2} = 4 \times T_{1} = 4 \times 273 = 1092 K T_{2} = 1092 - 273 T_{2} = 819^{\circ} C$
Hence, the temperature is $T_{2} = 819^{\circ} C$ .

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