MHT CET · Physics · Waves and Sound
At what temperature will the speed of sound be nearly 1.5 times its value at N.T.P.?
- A \(136^{\circ} \mathrm{C}\)
- B \(614^{\circ} \mathrm{C}\)
- C \(341^{\circ} \mathrm{C}\)
- D \(409^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(341^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
Speed of sound depends on \(T\) temperature, \(M\) molar mass and \(\gamma\) gas exponent:
\(\begin{aligned}
& v=\sqrt{\frac{\gamma R T}{M}} \\
& \Rightarrow \frac{v^{\prime}}{v}=\sqrt{\frac{T^{\prime}}{T}}=1.5 \\
& \Rightarrow \sqrt{T^{\prime}}=1.5 \sqrt{(273)} \\
& T^{\prime}=2.25 \times 273 \mathrm{~K}=614 \mathrm{~K}
\end{aligned}\)
On writing in degree Celsius:
\(T^{\prime}=341^{\circ} \mathrm{C}\)
\(\begin{aligned}
& v=\sqrt{\frac{\gamma R T}{M}} \\
& \Rightarrow \frac{v^{\prime}}{v}=\sqrt{\frac{T^{\prime}}{T}}=1.5 \\
& \Rightarrow \sqrt{T^{\prime}}=1.5 \sqrt{(273)} \\
& T^{\prime}=2.25 \times 273 \mathrm{~K}=614 \mathrm{~K}
\end{aligned}\)
On writing in degree Celsius:
\(T^{\prime}=341^{\circ} \mathrm{C}\)
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