Question

At what temperature the speed of sound in air will be $1.5$ times its values at ${27}^{\circ }C$ in air?

• A. ${102}^{\circ }C$
• B. ${204}^{\circ }K$
• C. ${204}^{\circ }C$
• D. ${402}^{\circ }C$

Answer 1

Answer: (D)

${402}^{\circ }C$

$V_T=\sqrt{\frac{{\gamma }_{air}RT}{M}}$

$V_{300K}=\sqrt{\frac{{\gamma }_{air}R300}{M}}$

$\frac{V_T}{V_{300K}}=\frac{3}{2}=\sqrt{\frac{T}{300}}$

$T=\frac{9}{4}\times 300=675K$

$t=T-273=675-273={402}^{\circ }C$