Question

If the velocity of sound in a gas is 200 m s${}^{-1}$ when the temperature is ${127}^{\circ }C$, then the velocity of sound in the same gas when temperature is increased by ${900}^{\circ }F$ is :

• A. $200\sqrt{3}$
• B. $300$
• C. $100\sqrt{5}$
• D. $450$

Answer 1

The correct option is B $300$

The speed of sound in a gas is given by $v=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\gamma RT}$

Hence, $v\propto \sqrt{T}\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$

Given $v_1=200\text{m/s},T_1={127}^{\circ }C=127+273=400\text{K}$

Final temperature of gas $T_2=T_1+{900}^{\circ }F=(400+\frac{5}{9}\times 900)\text{K}=900\text{K}$

Thus, $v_2=v_1\times \sqrt{\frac{T_2}{T_1}}=200\times \sqrt{\frac{900}{400}}=300\text{m/s}$