Find the velocity of sound in air at NTP. The density of air is `1.29kgm^(-3), gamma` for this is 1.42?

Answer

To find the velocity of sound in air at Normal Temperature and Pressure (NTP), we can use the formula:

\[ v = \sqrt{\frac{\gamma P}{\rho}} \]

Where:
- \( v \) is the velocity of sound,
- \( \gamma \) is the adiabatic index (given as 1.42),
- \( P \) is the pressure (given as \( 1.01 \times 10^5 \, \text{Pa} \)),
- \( \rho \) is the density of air (given as \( 1.29 \, \text{kg/m}^3 \)).

### Step-by-Step Solution:

1. **Identify the given values**:
- \( \gamma = 1.42 \)
- \( P = 1.01 \times 10^5 \, \text{Pa} \)
- \( \rho = 1.29 \, \text{kg/m}^3 \)

2. **Substitute the values into the formula**:
\[ v = \sqrt{\frac{1.42 \times (1.01 \times 10^5)}{1.29}} \]

3. **Calculate the numerator**:
- First, calculate \( 1.42 \times (1.01 \times 10^5) \):
\[ 1.42 \times 1.01 \times 10^5 = 1.43242 \times 10^5 \, \text{Pa} \]

4. **Divide by the density**:
\[ \frac{1.43242 \times 10^5}{1.29} \approx 1.109 \times 10^5 \]

5. **Take the square root**:
\[ v = \sqrt{1.109 \times 10^5} \approx 333.33 \, \text{m/s} \]

### Final Answer:
The velocity of sound in air at NTP is approximately \( 333.33 \, \text{m/s} \).

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