To solve the question, we will analyze both the assertion and the reason provided in the statement.
### Step-by-Step Solution:
1. **Understanding the Assertion**:
- The assertion states that the root mean square (RMS) velocity \( V_{\text{rms}} \) and the mean velocity \( V_{\text{mean}} \) of gaseous molecules are nearly of the order of the velocity of sound in a gas.
- The formulas for these velocities are:
- \( V_{\text{rms}} = \sqrt{\frac{3RT}{M}} \)
- \( V_{\text{mean}} = \sqrt{\frac{8RT}{\pi M}} \)
- The velocity of sound in a gas is given by:
- \( V_{\text{sound}} = \sqrt{\frac{\gamma RT}{M}} \)
- Here, \( R \) is the universal gas constant, \( T \) is the absolute temperature, \( M \) is the molar mass of the gas, and \( \gamma \) (gamma) is the adiabatic index (ratio of specific heats).
2. **Comparing Velocities**:
- All three velocities (RMS, mean, and sound) depend on the same parameters: \( R \), \( T \), and \( M \).
- Therefore, it can be concluded that \( V_{\text{rms}} \), \( V_{\text{mean}} \), and \( V_{\text{sound}} \) are indeed of the same order of magnitude.
3. **Understanding the Reason**:
- The reason states that sound travels in air due to vibrational molecular motion.
- Sound is a mechanical wave that propagates through the medium (air, in this case) due to the interactions between molecules, which vibrate around their equilibrium positions.
- This molecular motion is essential for the transmission of sound waves.
4. **Evaluating the Relationship**:
- While both the assertion and the reason are correct, the reason does not directly explain why \( V_{\text{rms}} \) and \( V_{\text{mean}} \) are of the same order as the velocity of sound.
- The assertion is about the relationship between molecular speeds and sound speed, while the reason describes the mechanism of sound propagation.
5. **Conclusion**:
- Both the assertion and the reason are correct statements, but the reason does not adequately explain the assertion. Therefore, the correct choice is that both statements are true, but the reason is not a valid explanation for the assertion.
### Final Answer:
- Assertion is correct, Reason is correct, but Reason is not a true explanation for Assertion.
