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

If the temperature of the gaseous medium drops by $1\%$, the velocity of sound in that medium
  1. increases by $5\%$
  2. remains unchanged
  3. decreases by $0.5\%$
  4. decreases by $2\%$

Solution

Velocity of sound in gaseous medium, $v = \sqrt{\frac{\gamma RT}{M}}$ or $v \propto T^{1/2}$ For small percentage change, % decrease in $v = \frac{1}{2} (\text{\% decrease in } T) = \frac{1}{2}(1\%) = 0.5\%$

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