Concept:The propagation speed of sound in an ideal gas depends on its thermodynamic properties and inertial mass.
Formula:$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:- According to Boyle's law, for a gas at a constant temperature, its density (\( \rho \)) is directly proportional to its pressure (\( P \)).
- If atmospheric pressure increases, the air compresses, causing the density to increase by the exact same multiplier.
- Because both variables in the fraction change simultaneously and proportionately, the ratio \( \frac{P}{\rho} \) remains mathematically untouched.
- Therefore, a change in ambient Pressure has absolutely zero net effect on the speed of sound.
Why other options are incorrect:Different media (solids vs gases) drastically change speed. Higher temperatures increase speed. Changes in pure density (e.g., adding moisture without changing pressure) directly alter speed.
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