Question

If the temperature of the medium drops by $1$ %, the velocity of sound in that medium

• A. increases by $5$ %
• B. remains unchanged
• C. decreases by $0.5$ %
• D. decreases by $2$ %

Answer 1

The correct option is C decreases by $0.5$ %

Velocity of sound is a medium $v\propto \sqrt{T}$

Thus percentage change in velocity of sound $\frac{\Delta v}{v}\times 100=\frac{1}{2}\frac{\Delta T}{T}\times 100$

$\therefore$ $\frac{\Delta v}{v}\times 100=\frac{1}{2}\times (-1)=-0.5$ %

Thus velocity of sound decreases by $0.5$%.