An observer saw a flash of lightning and after 8 seconds heard the thunder. If the average temperature of air is `17^@C`, how far away did the lightning occur ? Velocity of sound in air at `0^@C" is 331 ms"^(-1)`.

Answer

To find out how far away the lightning occurred, we can follow these steps:

### Step 1: Calculate the speed of sound at 17°C
The formula to calculate the speed of sound at a temperature \( T \) in Celsius is given by:

\[ V = V_0 \times \sqrt{\frac{T + 273}{273}} \]

where:
- \( V_0 \) is the speed of sound at 0°C (331 m/s),
- \( T \) is the temperature in Celsius (17°C).

First, we convert 17°C to Kelvin:

\[ T = 17 + 273 = 290 \text{ K} \]

Now, substituting the values into the formula:

\[ V = 331 \times \sqrt{\frac{290}{273}} \]

Calculating the square root:

\[ \sqrt{\frac{290}{273}} \approx 1.030 \]

Now, substituting this back into the equation for \( V \):

\[ V \approx 331 \times 1.030 \approx 341.15 \text{ m/s} \]

### Step 2: Calculate the distance to the lightning
The distance \( D \) can be calculated using the formula:

\[ D = V \times t \]

where:
- \( V \) is the speed of sound we just calculated (341.15 m/s),
- \( t \) is the time taken for the sound to travel (8 seconds).

Substituting the values:

\[ D = 341.15 \times 8 \]

Calculating the distance:

\[ D \approx 2729.2 \text{ meters} \]

### Conclusion
The lightning occurred approximately 2729.2 meters away from the observer.

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