(A): Speed of sound in a gas is independent of changes in pressure of the medium at a given temperature.
(R): A change in pressure of a gas is always accompanied by a change in density so that their ratio is always constant at a given temperature.

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To analyze the given assertion and reason statements, we will break down the problem step by step.

### Step 1: Understand the Assertion
The assertion states: "Speed of sound in a gas is independent of changes in pressure of the medium at a given temperature."

**Explanation**: The speed of sound in a gas can be described by the formula:
\[ v = \sqrt{\frac{\gamma P}{\rho}} \]
where \( v \) is the speed of sound, \( \gamma \) is the adiabatic index, \( P \) is the pressure, and \( \rho \) is the density of the gas.

At a constant temperature, if the pressure increases, the density also increases due to the ideal gas law (PV = nRT). However, the ratio \( \frac{P}{\rho} \) remains constant at a given temperature. Therefore, the speed of sound does not change with pressure at constant temperature.

### Step 2: Understand the Reason
The reason states: "A change in pressure of a gas is always accompanied by a change in density so that their ratio is always constant at a given temperature."

**Explanation**: According to the ideal gas law, when the temperature is constant, any change in pressure will result in a proportional change in density. This means that while both pressure and density change, their ratio \( \frac{P}{\rho} \) remains constant, which is a key point in understanding why the speed of sound does not depend on pressure.

### Step 3: Evaluate Both Statements
- The assertion is true because the speed of sound in a gas is indeed independent of pressure changes at a constant temperature.
- The reason is also true as it correctly explains the relationship between pressure and density at constant temperature.

### Step 4: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that:

**Final Answer**: Both assertion and reason are true, and the reason is the correct explanation of the assertion.