Calculate the difference in the speeds of sound in air at `- 3^(@) c`,`60 cm` pressure of mercury and `30^(@) c`, `75 cm` pressure of mercury. The speed of sound in air at `0^(@)C` is `332 m//s`.

Explanation

To solve the problem of calculating the difference in the speeds of sound in air at two different temperatures and pressures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of sound at 0°C, \( V_0 = 332 \, \text{m/s} \)
- Temperature 1, \( T_1 = -3°C \)
- Pressure 1, \( P_1 = 60 \, \text{cm Hg} \)
- Temperature 2, \( T_2 = 30°C \)
- Pressure 2, \( P_2 = 75 \, \text{cm Hg} \)

2. **Calculate Speed of Sound at \( T_1 \):**
The formula to calculate the speed of sound at a given temperature is:
\[ V_1 = V_0 + 0.61 \times T_1 \]
Substituting the values:
\[ V_1 = 332 + 0.61 \times (-3) \]
\[ V_1 = 332 - 1.83 = 330.17 \, \text{m/s} \]

3. **Calculate Speed of Sound at \( T_2 \):**
Using the same formula:
\[ V_2 = V_0 + 0.61 \times T_2 \]
Substituting the values:
\[ V_2 = 332 + 0.61 \times 30 \]
\[ V_2 = 332 + 18.3 = 350.3 \, \text{m/s} \]

4. **Calculate the Difference in Speeds:**
The difference in speeds is calculated as:
\[ \Delta V = V_2 - V_1 \]
Substituting the values:
\[ \Delta V = 350.3 - 330.17 = 20.13 \, \text{m/s} \]

5. **Final Result:**
The difference in the speeds of sound in air at the given conditions is:
\[ \Delta V = 20.13 \, \text{m/s} \]