Working with sound waves

(1)The pitch of an organ pipe, F is proportional to V, the velocity of sound in air. The velocity of sound in air increases as the temperature increases according to the relation V proportional to T^(1/2). Hence F is proportional to T^0.5

The density of dry air is greater than that of humid air. As the humidity increases, the velocity of sound in air increases, even though r (Gamma, ratio of specific heats) for the mixture of air and water vapour is less than for dry air. hence the pitch somewaht increases with humidity.

(2) This is due to refraction of sound in the atmospheric layers of varying density. At night, the earth cools rapidly, while the atmosphere is warmer. Since the temperature increases with altitude, the velocity of sound increases with altitude and the sound waves are bent towards the ground

(3) The temperature changes need not be equal in magnitude. The temperature changes are inversely proportional to their heat capacities.

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