Sound Speed and Humidity – Rankers Physics
Topic: Waves
Subtopic: Sound Wave and its Characteristics

Sound Speed and Humidity

Assertion (A): Sound travels faster on a rainy day than on a dry day.
Reason (R): With increase in humidity pressure increases.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

The speed of sound in a gas is \( v = \sqrt{\gamma P/\rho} \). Moist air (humid air) has a lower average molecular mass and thus lower density \( \rho \) than dry air at the same pressure and temperature. A lower density leads to a higher speed of sound. Thus, A is true. Reason R is false; increasing humidity does not necessarily increase total pressure, and the primary factor for faster sound is reduced density.

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