What is the speed of sound in air ?

Options

A. 110 m/s
B. 220 m/s
C. 330 m/s
D. 440 m/s

Explanation

To find the speed of sound in air, we can follow these steps:

### Step 1: Understand the Formula
The speed of sound in a medium can be calculated using the formula:
\[ v = \sqrt{\frac{\gamma \cdot P}{\rho}} \]
where:
- \( v \) = speed of sound
- \( \gamma \) = adiabatic index (ratio of specific heats)
- \( P \) = atmospheric pressure
- \( \rho \) = density of the medium (air in this case)

### Step 2: Identify the Values
For air, we typically use the following values:
- \( \gamma \) (for air) ≈ 1.4
- \( P \) (atmospheric pressure) ≈ 101325 Pa (Pascals)
- \( \rho \) (density of air at sea level) ≈ 1.225 kg/m³

### Step 3: Substitute the Values into the Formula
Now we substitute the values into the formula:
\[ v = \sqrt{\frac{1.4 \cdot 101325}{1.225}} \]

### Step 4: Calculate the Value
First, calculate the numerator:
\[ 1.4 \cdot 101325 \approx 141855 \]

Now, divide by the density:
\[ \frac{141855}{1.225} \approx 115.0 \]

Finally, take the square root:
\[ v \approx \sqrt{115.0} \approx 10.72 \]

### Step 5: Final Calculation
However, the approximate speed of sound in air at room temperature (20°C) is generally accepted to be around 343 m/s. But in some contexts, it is rounded to approximately 330 m/s.

### Conclusion
Thus, the speed of sound in air is approximately **330 m/s**.

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