When height increases, velocity of sound decreases: (a) this...

When height increases, velocity of sound decreases:
(a) this is due to decrease of pressure
(b) this is due to decrease in temperature
(c) this is due to both decrease in temperature and pressure
(d) statement is wrong

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Key Concepts

Speed of Sound in Gases

The speed of sound in a gas is determined by the medium's physical properties and is calculated by the formula v = ?(?RT/M), where ? is the adiabatic index, R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas. This relationship fundamentally shows that sound speed depends on the medium’s temperature and composition rather than directly on pressure alone.

Temperature Dependence

Temperature plays a crucial role in determining the speed of sound in gases because it directly affects the kinetic energy of the gas molecules. As the temperature increases, molecules move faster, resulting in a higher speed of sound, and conversely, a decrease in temperature leads to a reduction in the velocity of sound.

Pressure and Density Relationship

In a gas, pressure and density are related through the ideal gas law. While both pressure and density decrease with altitude, their effects cancel out in the calculation of the speed of sound. Therefore, variations in the speed of sound with altitude are primarily due to changes in temperature, not pressure.

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