At what temperature does the velocity of sound in air increases by 2% in comparison with velocity at…
At what temperature does the velocity of sound in air increases by 2% in comparison with velocity at $0^\circ\mathrm{C}$?
Solution
Sol. Let $t^\circ\mathrm{C}$ be the required temperature, $v_0$ the speed of sound at $0^\circ\mathrm{C}$ and $v_t$ the speed at $t^\circ\mathrm{C}$.
As, $v\propto\sqrt{T}$
$\Rightarrow \dfrac{v_t}{v_0}=\sqrt{\dfrac{t+273}{273}}$
But $v_t=v_0+\dfrac{2}{100}v_0=v_0(1+0.02)=(1.02)v_0$
$\therefore \dfrac{(1.02)v_0}{v_0}=\sqrt{\dfrac{t+273}{273}}$
$t+273=(1.02)^2\times273=1.0404\times273$
$\Rightarrow t=284.02-273\Rightarrow t=11.02^\circ\mathrm{C}$
Answer: $t=11.02^\circ\mathrm{C}$