Question

Speed of sound in a gas at ${27}^{\circ }C$ is $360\text{m/s}$. Its speed at ${37}^{\circ }C$ is

• A. $360\text{m/s}$
• B. $363\text{m/s}$
• C. $366\text{m/s}$
• D. $372\text{m/s}$

Answer 1

The correct option is C $366\text{m/s}$

As we know that
Speed, $v\propto \sqrt{T}$ where, $T$ is in kelvin.
$\Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}=\sqrt{\frac{310}{300}}={\left[\frac{300+10}{300}\right]}^{\frac{1}{2}}={(1+\frac{1}{30})}^{\frac{1}{2}}$
From binomial expansion it can be written as
$\frac{v_2}{v_1}={(1+\frac{1}{30})}^{\frac{1}{2}}=1+\frac{1}{60}$
or, $v_2=v_1+\frac{v_1}{60}=360+\frac{360}{60}=366\text{m/s}$