Concept:The speed of sound in an ideal gas is governed by the ratio of its pressure to its density.
Formula:$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:- According to Boyle's law (\( P \propto \rho \)), if you isothermally increase the pressure of a gas, its density increases by the exact same proportion.
- Because both \( P \) (numerator) and \( \rho \) (denominator) increase together, their ratio \( P/\rho \) remains mathematically constant.
- Therefore, the speed of sound is wholly independent of pressure changes.
Why other options are incorrect:Sound speed heavily depends on Temperature (increases speed) and absolute Density (different gases have different speeds). (Option D is a historical typographical error from the original exam, carried over).
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