(A): The velocity of sound changes as we go up in the atmosphere.
(R): Pressure decreases as we go up in the atmosphere.

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 assertion and reason provided in the question, we can break down the problem step by step.

### Step 1: Understanding the Assertion
The assertion states that "The velocity of sound changes as we go up in the atmosphere."

**Explanation:**
The velocity of sound in a medium depends on various factors, including temperature, pressure, and density. As we ascend in the atmosphere, the temperature generally decreases, which can affect the speed of sound.

### Step 2: Understanding the Reason
The reason states that "Pressure decreases as we go up in the atmosphere."

**Explanation:**
It is a well-known fact that atmospheric pressure decreases with altitude. As we go higher in the atmosphere, the density of air also decreases, which contributes to the change in pressure.

### Step 3: Analyzing the Relationship
Now, we need to analyze whether the reason provided is a correct explanation for the assertion.

**Velocity of Sound Formula:**
The velocity of sound \( v \) in a medium can be expressed as:
\[ v = \sqrt{\frac{\gamma P}{\rho}} \]
Where:
- \( \gamma \) = adiabatic index (constant for a given gas)
- \( P \) = pressure
- \( \rho \) = density

As pressure decreases with altitude, density also decreases. However, the relationship between velocity, pressure, and density is not straightforward because both pressure and density decrease.

### Step 4: Alternative Formula
Another formula for the velocity of sound is:
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
Where:
- \( R \) = gas constant
- \( T \) = temperature
- \( M \) = molecular mass

This formula shows that the velocity of sound is more directly related to temperature than to pressure or density. As long as the temperature remains constant, the velocity of sound does not change significantly with pressure or density.

### Step 5: Conclusion
- The assertion is true: the velocity of sound does change as we go up in the atmosphere.
- The reason is also true: pressure decreases as we go up in the atmosphere.
- However, the reason does not correctly explain the assertion because the velocity of sound is primarily influenced by temperature rather than pressure alone.

### Final Answer
Both the assertion (A) and reason (R) are true, but R is not the correct explanation for A.

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