Question

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

Answer 1

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.
$v\propto \sqrt{T}$
∴​
$$\begin{gathered} \frac{{v_2}^2}{{v_1}^2}=\frac{T_2}{T_1} \\ \Rightarrow \frac{{\left(2v_1\right)}^2}{{v_1}^2}=\frac{T_2}{273} \\ \Rightarrow T_2=273\times 4=1092\mathrm{K} \end{gathered}$$
To convert Kelvin into degree celsius:
$T_2=\left(273\times 4\right)-273=819°\mathrm{C}$
Hence, the temperature (T₂ ) will be 819˚ C