Question

At what temperature (in ${}^{\circ }\text{C}$) will the velocity of sound in air be $1.5$ times its velocity at $0{}^{\circ }\text{C}$? (The velocity of sound in air at $0{}^{\circ }\text{C}=330{\text{m s}}^{-1}$)

• A. $409.50{}^{\circ }\text{C}$
• B. $614.25{}^{\circ }\text{C}$
• C. $136.50{}^{\circ }\text{C}$
• D. $341.25{}^{\circ }\text{C}$

Answer 1

The correct option is D $341.25{}^{\circ }\text{C}$

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 $1.5$ times the value of ${\text{v}}_0$, be $\text{T}$
So, ${\text{v}}_{\text{T}}=1.5\times 330=495{\text{m s}}^{-1}$
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: $\frac{{\text{v}}_{\text{T}}}{{\text{v}}_0}=1.5$

$⟹(1.5{)}^2=\frac{\text{T}}{273}$

$⟹\text{T}=273\times 2.25=614.25\text{K}$

In Celsius scale, $\text{T}=614.25-273=341.25{}^{\circ }\text{C}$