In given gaseous medium, at what temperature, the velocity of sound will be double that of velocity at…
In given gaseous medium, at what temperature, the velocity of sound will be double that of velocity at $27^\circ\mathrm{C}$?
Solution
Sol. Given, velocity of sound, $v_2=2v_1$
Temperature, $T_1=27^\circ\mathrm{C}=(27+273)=300\ \mathrm{K}$
As, $v\propto\sqrt{T}$
$\Rightarrow \dfrac{v_1}{v_2}=\sqrt{\dfrac{T_1}{T_2}}\Rightarrow \dfrac{v_1}{2v_1}=\sqrt{\dfrac{300}{T_2}}$
$\Rightarrow T_2=1200\ \mathrm{K}\ \text{or}\ T_2=927^\circ\mathrm{C}$
Answer: $T_2=1200\ \mathrm{K}\ \text{or}\ T_2=927^\circ\mathrm{C}$
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