At what temperature does the velocity of sound in air increased by 10% comparison with velocity at…
At what temperature does the velocity of sound in air increased by 10% comparison with velocity at $0^{\circ} \mathrm{C}$ ?
- $45^{\circ} \mathrm{C}$
- $57^{\circ} \mathrm{C}$
- $27^{\circ} \mathrm{C}$
- $18^{\circ} \mathrm{C}$
Solution
Speed of sound in air is directly proportional to the square root of temperature.
i.e.
$
v_1 \propto \sqrt{T_1} ...(i)
$
$v_2 \propto \sqrt{T_2}$...(ii)
Now, $\quad \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
At $0^{\circ} \mathrm{C}, T_1=273 \mathrm{~K}$
Increase in velocity $=10 \%$
i.e., $v_2=\frac{11}{10} v_1$
$\begin{array}{rlrl} & \text { Hence, } & \frac{v_1}{\frac{11}{10} v_1} & =\sqrt{\frac{273}{T_2}} \\ \Rightarrow & \frac{10}{11} & =\sqrt{\frac{273}{T_2}} \Rightarrow \frac{100}{121}=\frac{273}{T_2} \\ \Rightarrow & & T_2 & =\frac{273 \times 121}{100} \\ & & =330.33 \mathrm{~K}=57.33^{\circ} \mathrm{C} \simeq 57^{\circ} \mathrm{C}\end{array}$
Asked in: AP EAMCET 2021 (25 Aug Shift 2)
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