Question

When the temperature of air rises by $3K$ from $300K$, what is the percentage rise in the velocity of sound?

• A. $0.5$%
• B. $1$%
• C. $2$%
• D. None of these

Answer 1

The correct option is A $0.5$%

Velocity of sound is proportional to the square root of the temperature of air.

$⟹v\propto \sqrt{T}$

$⟹\frac{v^{\prime }}{v}=\sqrt{\frac{T^{\prime }}{T}}$

Thus percentage rise in velocity=$\frac{v^{\prime }-v}{v}\times 100$%
$=\frac{\sqrt{\frac{T^{\prime }}{T}}-1}{1}\times 100$

$=\frac{\sqrt{\frac{303}{300}}-1}{1}\times 100$

% = $0.5$%