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A : Velocity of sound in air increased w...

A : Velocity of sound in air increased with increase in humidity .
R : Velocity of sound doesn't depend upon medium .

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To analyze the given assertion (A) and reason (R), we need to evaluate both statements regarding the velocity of sound in air and its dependence on the medium. ### Step 1: Understanding the Assertion (A) The assertion states that "the velocity of sound in air increases with an increase in humidity." - **Explanation**: When humidity increases, the amount of water vapor in the air increases. Water vapor is less dense than the nitrogen and oxygen that make up most of the air. As a result, the overall density of the air decreases with increased humidity. ### Step 2: Understanding the Relationship Between Velocity and Density The velocity of sound in a medium is given by the formula: \[ v = \sqrt{\frac{B}{\rho}} \] where \( v \) is the velocity of sound, \( B \) is the bulk modulus of the medium, and \( \rho \) is the density of the medium. - **Explanation**: Since the bulk modulus of air does not change significantly with humidity, a decrease in density (due to increased humidity) leads to an increase in the velocity of sound. ### Step 3: Evaluating the Reason (R) The reason states that "the velocity of sound doesn't depend upon the medium." - **Explanation**: This statement is incorrect. The velocity of sound does depend on the medium through which it travels. Different media (like air, water, or solids) have different densities and bulk moduli, which affect the speed of sound. ### Conclusion - **Assertion (A)** is **True**: The velocity of sound in air does increase with an increase in humidity due to the decrease in density. - **Reason (R)** is **False**: The velocity of sound does depend on the medium. ### Final Answer The correct answer is that Assertion (A) is true, and Reason (R) is false. ---
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