According to Newton's formula, the speed of sound in air at STP is
(Take the mass of 1 mole of air is `29 xx 10^(-3)` kg)

Options

A. `250ms^(-1)`
B. `260ms^(-1)`
C. `270ms^(-1)`
D. `280ms^(-1)`

Explanation

To find the speed of sound in air at STP according to Newton's formula, we will follow these steps:

### Step 1: Understand the parameters
We know that:
- The mass of 1 mole of air = \(29 \times 10^{-3}\) kg
- At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters or \(22.4 \times 10^{-3}\) m³.

### Step 2: Calculate the density of air
The density (\(\rho\)) of air at STP can be calculated using the formula:
\[ \rho = \frac{\text{mass of 1 mole of air}}{\text{volume of 1 mole of air at STP}} \]
Substituting the values:
\[ \rho = \frac{29 \times 10^{-3} \text{ kg}}{22.4 \times 10^{-3} \text{ m}^3} = \frac{29}{22.4} \text{ kg/m}^3 \]
Calculating this gives:
\[ \rho \approx 1.29 \text{ kg/m}^3 \]

### Step 3: Determine the pressure at STP
At STP, the pressure (\(P\)) is:
\[ P = 1 \text{ atm} = 1.01 \times 10^5 \text{ N/m}^2 \]

### Step 4: Use the formula for the speed of sound
According to Newton's formula, the speed of sound (\(v\)) in a medium can be calculated using the formula:
\[ v = \sqrt{\frac{P}{\rho}} \]
Substituting the values of pressure and density:
\[ v = \sqrt{\frac{1.01 \times 10^5 \text{ N/m}^2}{1.29 \text{ kg/m}^3}} \]

### Step 5: Calculate the speed of sound
Calculating the above expression:
\[ v = \sqrt{\frac{1.01 \times 10^5}{1.29}} \approx \sqrt{78255.04} \approx 280 \text{ m/s} \]

### Final Answer
The speed of sound in air at STP is approximately \(280 \text{ m/s}\).

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