Question

At what temperature (in ${}^{\circ }\text{C}$) will the velocity of sound in air be triple its velocity at $0{}^{\circ }\text{C}$? (The velocity of sound in air at $0{}^{\circ }\text{C}=330{\text{m s}}^{-1}$)

• A. 2184

Answer 1

The correct option is A 2184
Velocity of sound in air at $0{}^{\circ }\text{C}$ is, ${\text{v}}_0=330{\text{m s}}^{-1}$
Let the temperature at which the velocity of sound is thrice the value of ${\text{v}}_0$, be $\text{T}$
So, ${\text{v}}_{\text{T}}=3\times 330=990{\text{m s}}^{-1}$
The temperature should be in kelvin ($\text{K}$) with $0{}^{\circ }\text{C}=273\text{K}$
We know that,
$\text{v}\propto \sqrt{\text{T}}$

$\frac{{\text{v}}_{\text{T}}}{{\text{v}}_0}=\sqrt{\frac{\text{T}}{273}}$

Given: $\frac{{\text{v}}_{\text{T}}}{{\text{v}}_0}=3$

$⟹3^2=\frac{\text{T}}{273}$

$⟹\text{T}=273\times 9=2457\text{K}$

In Celsius scale, $\text{T}=2457-273=2184{}^{\circ }\text{C}$