A lightning flash is seen in the sky and 8.2 s later the boom of the thunder is heard. The temperature of the air is \(12^{\circ} \mathrm{C}\) (a) What is the speed of sound at that temperature? [Hint: Light is an electromagnetic wave that travels at a speed of $3.00 \times 10^{8} \mathrm{m} / \mathrm{s} .1$ (b) How far away is the lightning strike?

We can use the formula for the speed of sound in dry air, which is given by: $$ v = 331.3 + 0.606(T) $$ where \(v\) is the speed of sound in meters per second (m/s), and \(T\) is the temperature in degrees Celsius. Given the air temperature is \(12^{\circ} \mathrm{C}\), we can find the speed of sound at this temperature: $$ v = 331.3 + 0.606(12) $$

Plug the temperature value into the expression and calculate the speed of sound: $$ v = 331.3 + 0.606 \times 12 = 331.3 + 7.272 = 338.572 \,\text{m/s} $$ Hence, the speed of sound at the given temperature of \(12^{\circ} \mathrm{C}\) is \(338.572\) m/s.

We know the time difference between the lightning flash being seen and the thunder being heard is \(8.2\) seconds. Since light travels at a speed of \(3.00 \times 10^{8} \,\text{m/s}\), and we can assume light reaches us almost instantly, the time taken can be approximated as the time taken for the sound to travel from the lightning strike to the observer. We can use the speed of sound to find the distance using the formula: $$ \text{Distance} = v \times t $$ where \(\text{Distance}\) : distance from the lightning strike to the observer, \(v\) : speed of sound (determined in Step 2), \(t\) : time difference, which is given as \(8.2\) seconds. Calculate the distance: $$ \text{Distance} = 338.572 \,\text{m/s} \times 8.2 \,\text{s} = 2774.2904 \,\text{m} $$

The distance between the observer and the lightning strike is approximately \(2774.2904 \,\text{m}\) or \(2.774 \,\text{km}\).