Sound Speed and Humidity – Rankers Physics

Sound Wave and its Characteristics: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Sound Wave and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

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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