Concept:The velocity of sound in gases relies heavily on the gas's internal restoring forces and mass, expressed mathematically by Laplace.
Formula:$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:- According to gas laws, pressure and density are directly proportional at a constant temperature.
- If you mechanically squeeze a gas to increase its pressure (\( P \)), the gas compresses, shrinking its volume and increasing its density (\( \rho \)) by the exact same multiplier.
- Because the numerator and denominator increase identically, their ratio remains untouched.
- Consequently, the calculated speed of sound must remain the same.
Why other options are incorrect:Students incorrectly guess Option A by looking at \( P \) in the numerator of the formula but neglecting the invisible dependency of \( \rho \) on pressure.
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