Concept:The velocity of sound in an ideal gas relies on the ratio of pressure to density.
Formula:$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:- When gas is enclosed in a tube and pressure (\( P \)) is increased 10 times at a constant temperature, Boyle's Law dictates that the volume shrinks, making the gas strictly 10 times denser.
- The new velocity would be \( v' = \sqrt{\frac{\gamma (10P)}{(10\rho)}} \).
- The 10s perfectly cancel out, leaving the original ratio intact.
- Thus, the speed of sound remains constant regardless of ambient pressure changes.
Why other options are incorrect:Students often glance at the formula, see \( P \) in the numerator, and wrongly assume an increase (Option A) without accounting for the hidden proportional variable \( \rho \).
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