Question

The speed of sound as measured by a student in the laboratory on a winter day is $340m{s}^{-1}$ when the room temperature is ${17}^{\circ }C$. What speed will be measured by another student repeating the experiment on a day when the room temperature is ${32}^{\circ }C$ ?

Answer 1

$V_1=340m/s,V_2=?$

$T_1=273+17$

=290 K,

$T_2=273+32=305K$

We know, $V=\frac{a}{\sqrt{T}}$

$\frac{V_1}{V_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$

$\Rightarrow V_2=\frac{\sqrt{V_1}\times \sqrt{T_2}}{\sqrt{T_1}}$

$=340\times \sqrt{\frac{350}{290}}$

=349 m/s