Question

If the speed of sound is changed by $1$ percent, the change in temperature of the air which was initially at $0$${}^o$C would be

• A. 5${}^o$C
• B. 6${}^o$C
• C. 5.5${}^o$C
• D. 6.5${}^o$C

Answer 1

The correct option is C 5.5${}^o$C

Speed of sound $\vartheta \propto \sqrt{T}$.
When speed of sound is changed by $1\%$
So, $\vartheta$ becomes $\vartheta \frac{101}{100}$
So, $\frac{{\vartheta }_1}{{\vartheta }_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$

$\frac{\vartheta }{\frac{101\vartheta }{100}}=\frac{\sqrt{273}}{\sqrt{273+t}}$

$\frac{100}{101}=\sqrt{\frac{273}{273+t}}$

$10000(273+t)=10201\left(273\right)$

$10000t=201\left(273\right)$

$t=\frac{201\left(273\right)}{10000}$$=5.5k$

So, temperature $=(273+5.5)K$$={5.5}^{0}C$