The velocity of sound in air at NTP is 331 m/s. Find its velocity when temperature eises to `91^(@)C` and its pressure is doubled.

Options

A. 372 m/s
B. 382.1 m/s
C. 423 m/s
D. 392.5 m/s

Explanation

To find the velocity of sound in air at a temperature of 91°C when the pressure is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between velocity, temperature, and pressure**:
The velocity of sound in air is given by the formula:
\[ V = \sqrt{\frac{\gamma P}{\rho}} \]
However, for our purposes, we can use the relationship that the velocity of sound is proportional to the square root of the temperature (in Kelvin) and independent of pressure.

2. **Convert temperatures from Celsius to Kelvin**:
- The initial temperature \( T_1 \) is 0°C, which is:
\[ T_1 = 0 + 273 = 273 \, \text{K} \]
- The final temperature \( T_2 \) is 91°C, which is:
\[ T_2 = 91 + 273 = 364 \, \text{K} \]

3. **Use the proportional relationship of velocities**:
Since the velocity of sound is proportional to the square root of the temperature, we can write:
\[ \frac{V_1}{V_2} = \sqrt{\frac{T_1}{T_2}} \]
Where \( V_1 \) is the initial velocity of sound at 0°C (331 m/s) and \( V_2 \) is the velocity we want to find.

4. **Substitute the known values into the equation**:
\[ \frac{331}{V_2} = \sqrt{\frac{273}{364}} \]

5. **Calculate the right side of the equation**:
First, calculate the fraction:
\[ \frac{273}{364} \approx 0.750 \]
Now take the square root:
\[ \sqrt{0.750} \approx 0.866 \]

6. **Rearrange the equation to solve for \( V_2 \)**:
\[ V_2 = \frac{331}{0.866} \approx 382.1 \, \text{m/s} \]

### Final Answer:
The velocity of sound in air at 91°C when the pressure is doubled is approximately **382.1 m/s**.