velocity of sound is measured in hydrogen and oxygen gases at a given temperature. The ratio of two velocities will be `(V_(H)//V_(0))`

Options

A. ` 1 : 4`
B. ` 4 : 1`
C. `1 : 1`
D. `32 : 1`

Explanation

To find the ratio of the velocities of sound in hydrogen gas (V_H) and oxygen gas (V_O) at a given temperature, we can use the relationship between the speed of sound in a gas and its molar mass. The speed of sound in a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The speed of sound (V) in a gas is given by the formula:
\[ V \propto \frac{1}{\sqrt{M}} \]
where \(M\) is the molar mass of the gas.

2. **Setting Up the Ratios**:
For hydrogen (H) and oxygen (O), we can express the velocities as:
\[ V_H \propto \frac{1}{\sqrt{M_H}} \quad \text{and} \quad V_O \propto \frac{1}{\sqrt{M_O}} \]
where \(M_H\) is the molar mass of hydrogen and \(M_O\) is the molar mass of oxygen.

3. **Calculating Molar Masses**:
- The molar mass of hydrogen (H) is approximately 1 g/mol.
- The molar mass of oxygen (O) is approximately 16 g/mol.

4. **Finding the Ratio of Velocities**:
To find the ratio of the velocities, we take:
\[ \frac{V_H}{V_O} = \frac{\sqrt{M_O}}{\sqrt{M_H}} \]
Substituting the molar masses:
\[ \frac{V_H}{V_O} = \frac{\sqrt{16}}{\sqrt{1}} = \frac{4}{1} \]

5. **Final Result**:
Thus, the ratio of the velocities of sound in hydrogen and oxygen is:
\[ \frac{V_H}{V_O} = 4:1 \]

### Conclusion:
The final answer is that the ratio of the velocities of sound in hydrogen to oxygen at a given temperature is \(4:1\).