At `10^5 Nm^(-2)` atmospheric pressure the density of air is `1.29 kg m^(-3)`.If `gamma=1.41` for air, calculate the speed of sound in air.

Answer

To calculate the speed of sound in air using the given values, we can use the formula:

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

where:
- \( v \) is the speed of sound,
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( P \) is the pressure,
- \( \rho \) is the density.

### Step-by-Step Solution:

1. **Identify the given values**:
- Atmospheric pressure \( P = 10^5 \, \text{N/m}^2 \)
- Density of air \( \rho = 1.29 \, \text{kg/m}^3 \)
- Adiabatic index \( \gamma = 1.41 \)

2. **Substitute the values into the formula**:
\[ v = \sqrt{\frac{1.41 \cdot 10^5}{1.29}} \]

3. **Calculate the numerator**:
- First, calculate \( 1.41 \cdot 10^5 \):
\[ 1.41 \cdot 10^5 = 141000 \, \text{N/m}^2 \]

4. **Divide by the density**:
\[ \frac{141000}{1.29} \approx 109296.69 \, \text{m}^2/\text{s}^2 \]

5. **Take the square root**:
\[ v = \sqrt{109296.69} \approx 330.6 \, \text{m/s} \]

### Final Result:
The speed of sound in air at the given conditions is approximately \( 330.6 \, \text{m/s} \).