when temperature in increased by `1^@ C ` velocity of sound in air increaeses by

Options

A. `0.61 ms ^(-1)`
B. `6.1 ms^(-1)`
C. `61 ms^(-1)`
D. `610 ms^(-1)`

Explanation

To solve the question of how much the velocity of sound in air increases when the temperature is raised by 1°C, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The velocity of sound in air is affected by temperature. The formula that relates the velocity of sound (V) to temperature (T) is given by:
\[ V_T = V_0 + 0.61 \times T \]
where \( V_0 \) is the velocity of sound at 0°C, and \( T \) is the temperature in degrees Celsius.

2. **Identify the Change in Temperature**: The problem states that the temperature is increased by \( \Delta T = 1°C \).

3. **Calculate the Change in Velocity**: To find the change in velocity (\( \Delta V \)) when the temperature increases by 1°C, we can differentiate the formula:
\[ \Delta V = 0.61 \times \Delta T \]
Substituting \( \Delta T = 1°C \):
\[ \Delta V = 0.61 \times 1 = 0.61 \text{ m/s} \]

4. **Conclusion**: Therefore, the increase in the velocity of sound in air when the temperature is raised by 1°C is:
\[ \Delta V = 0.61 \text{ m/s} \]

### Final Answer:
The velocity of sound in air increases by **0.61 m/s** when the temperature is increased by 1°C.

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