Calculate the increase velocity of sound for `1^@C` rise of temperature if the velocity of sound at `0^@C` is `332m//s`.

Options

A. `1.61 m//s`
B. `1 m//s`
C. `0.61 m//s`
D. None of these

Explanation

To calculate the increase in the velocity of sound for a rise of 1°C, we can use the formula that relates the velocity of sound in air to temperature:

\[ v = v_0 + (0.61 \, \text{m/s/°C}) \times \Delta T \]

Where:
- \( v \) is the velocity of sound at the new temperature.
- \( v_0 \) is the velocity of sound at 0°C (which is given as 332 m/s).
- \( \Delta T \) is the change in temperature (which is 1°C in this case).

### Step-by-Step Solution:

1. **Identify the given values:**
- Velocity of sound at 0°C, \( v_0 = 332 \, \text{m/s} \)
- Change in temperature, \( \Delta T = 1 \, \text{°C} \)

2. **Use the formula to calculate the increase in velocity:**
\[ \text{Increase in velocity} = 0.61 \, \text{m/s/°C} \times 1 \, \text{°C} \]

3. **Calculate the increase:**
\[ \text{Increase in velocity} = 0.61 \, \text{m/s} \]

4. **Calculate the new velocity of sound at 1°C:**
\[ v = v_0 + \text{Increase in velocity} \]
\[ v = 332 \, \text{m/s} + 0.61 \, \text{m/s} = 332.61 \, \text{m/s} \]

5. **Final Result:**
The increase in the velocity of sound for a rise of 1°C is \( 0.61 \, \text{m/s} \).

### Summary:
- The increase in velocity of sound for a 1°C rise in temperature is \( 0.61 \, \text{m/s} \).