Physics Waves ETEA 2017
PMDC Verified Question 109 of 125
The speed of sound in air at NTP is 300m/s. If the air pressure become 4 times then the speed of the sound will be
A
150m/s
B
300m/s
C
600m/s
D
None
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 300m/s
Concept:

The velocity of sound in an ideal gas depends solely on temperature and the gas's inherent properties, but it is independent of pressure.

Formula:

$$ v = \sqrt{\frac{\gamma P}{\rho}} $$

Solution:

  • According to Boyle's law (\( P \propto \rho \)), if you increase the pressure of a gas by a factor of 4, the gas gets compressed, causing its density (\( \rho \)) to also increase exactly by a factor of 4.


  • Because both numerator and denominator in Laplace's formula increase by the exact same multiplier, the ratio \( \frac{P}{\rho} \) remains mathematically constant.


  • Therefore, the speed remains 300 m/s.


Why other options are incorrect:

Option C assumes speed is directly proportional to pressure, incorrectly doubling the speed.

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