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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 statements, we need to evaluate both the assertion (A) and the reason (R) regarding the velocity of sound in air and its dependence on humidity and medium. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states that the velocity of sound in air increases with an increase in humidity. - Humidity refers to the amount of water vapor present in the air. When humidity increases, the proportion of water vapor in the air increases, which affects the density of the air. 2. **Density of Air and Water Vapor**: - The density of water vapor is less than that of dry air. Specifically, the density of water vapor is approximately \( \frac{5}{8} \) times the density of dry air. - Therefore, when humidity increases, the overall density of the air decreases because water vapor (which is lighter) replaces some of the heavier dry air. 3. **Velocity of Sound Formula**: - The speed of sound in a gas can be expressed as: \[ V = \sqrt{\frac{\gamma P}{\rho}} \] - Where \( V \) is the velocity of sound, \( \gamma \) is the adiabatic index (which depends on the medium), \( P \) is the pressure, and \( \rho \) is the density of the gas. 4. **Effect of Density on Velocity**: - From the formula, we can see that the speed of sound is inversely proportional to the square root of the density (\( \rho \)). - As humidity increases, the density (\( \rho \)) decreases, leading to an increase in the velocity of sound (\( V \)). 5. **Conclusion on Assertion**: - Since the assertion correctly states that the velocity of sound in air increases with an increase in humidity, we conclude that Assertion (A) is **true**. 6. **Understanding the Reason (R)**: - The reason states that the velocity of sound does not depend upon the medium. - This statement is incorrect because the speed of sound is indeed dependent on the medium through which it travels. The value of \( \gamma \) (the adiabatic index) varies for different media (e.g., air, water, solids). 7. **Conclusion on Reason**: - Since the reason is incorrect, we conclude that Reason (R) is **false**. ### Final Evaluation: - Assertion (A) is true, and Reason (R) is false. Therefore, the correct option is that A is true but R is false.
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