The velocity of sound in a tube containing air at $27^{o} C$ and a pressure of $76 c m$ of mercury is $330 m s^{- 1}$ . What will be its velocity, when the pressure is increased to $100 c m$ of mercury and the temperature is kept constant?

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Solution

The velocity(v) of sound in air is proportional to the square root of its pressure.
If the temperature is kept constant then we need not bother about it.
$\frac{v_{2}}{v_{1}} = \sqrt{\frac{P_{2}}{P_{1}}}$
$∴ v_{2} = v_{1} \times \sqrt{\frac{P_{2}}{P_{1}}} = 330 \times \sqrt{\frac{100}{76}} = 378.53$
The velocity will be 378.53m/s

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A glass tube, sealed at both ends, is 100 cm long. It lies horizontally with the middle 10 cm containing mercury. The two ends of the tube contain air at $27^{0}$ C and at a pressure 76 cm of mercury. The air column on one side is maintained at $0^{0}$ C and the other side is maintained at $127^{0}$ C. Calculate the length of the air column on the cooler side. Neglect the changes in the volume of mercury and of the glass.

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The velocity of sound in a tube containing air at 27oC and a pressure of 76cm of mercury is 330ms−1. What will be its velocity, when the pressure is increased to 100cm of mercury and the temperature is kept constant?

The velocity(v) of sound in air is proportional to the square root of its pressure.If the temperature is kept constant then we need not bother about it.v2v1=√P2P1∴v2=v1×√P2P1=330×√10076=378.53The velocity will be 378.53m/s

The velocity of sound in a tube containing air at $27^{o} C$ and a pressure of $76 c m$ of mercury is $330 m s^{- 1}$ . What will be its velocity, when the pressure is increased to $100 c m$ of mercury and the temperature is kept constant?