Assuming the temperatature to be constant, as we go up in the atmosphere, the velocity of sound

Options

A. increases
B. decreases
C. remains constant
D. first increases and then decreases

Answer

To solve the question regarding the velocity of sound as we go up in the atmosphere while assuming the temperature to be constant, we can follow these steps:

### Step 1: Understand the Formula for Velocity of Sound
The velocity of sound in a gas is given by the formula:
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( v \) = velocity of sound
- \( \gamma \) = adiabatic constant (ratio of specific heats)
- \( R \) = universal gas constant
- \( T \) = absolute temperature
- \( M \) = molecular mass of the gas

### Step 2: Analyze the Given Conditions
In the question, it is stated that the temperature \( T \) is constant as we go up in the atmosphere. This implies that \( R \), \( M \), and \( \gamma \) are also constants for a particular gas.

### Step 3: Substitute the Constants into the Formula
Since \( T \), \( R \), \( M \), and \( \gamma \) are all constants, we can conclude that the expression for the velocity of sound does not change with altitude. Therefore, the velocity of sound remains constant.

### Step 4: Conclusion
Based on the analysis, we can conclude that as we go up in the atmosphere, the velocity of sound remains constant under the assumption that the temperature is constant.

### Final Answer
The correct option is that the velocity of sound remains constant.

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