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At what temperature $\left(\right.$ in $\left.^{\circ} \mathrm{C}\right)$ will the speed of sound in air be 3 times its value at $0^{\circ} \mathrm{C}$ ?
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Verified Answer
As we know that,
The speed of sound in air $v \propto \sqrt{T}$
$$
\therefore \frac{v_T}{v_0}=\sqrt{\frac{T_T}{T_0}}=\sqrt{\frac{T_T}{273}}
$$
given that $\left(v_T=3 v_0\right)$
$$
\frac{3 v_0}{v_0}=\sqrt{\frac{T_T}{T_0}} \Rightarrow \frac{T_T}{273}=9
$$
So, $T_T=273 \times 9=2457 \mathrm{~K}$
$$
=2457-253=2184^{\circ} \mathrm{C}
$$
The speed of sound in air $v \propto \sqrt{T}$
$$
\therefore \frac{v_T}{v_0}=\sqrt{\frac{T_T}{T_0}}=\sqrt{\frac{T_T}{273}}
$$
given that $\left(v_T=3 v_0\right)$
$$
\frac{3 v_0}{v_0}=\sqrt{\frac{T_T}{T_0}} \Rightarrow \frac{T_T}{273}=9
$$
So, $T_T=273 \times 9=2457 \mathrm{~K}$
$$
=2457-253=2184^{\circ} \mathrm{C}
$$
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