A physicist at a fireworks display times the lag between seeing an explosion and hearing its sound, and finds it to be 0.800 s.

(a) How far (m)away is the explosion if air temperature is 22.0°C, neglecting the time taken for light to reach the physicist?

(b) How much further (m)away would the explosion be calculated to be if the speed of light is taken into account?

Vs = 332 m/s @ 0oC. = Velocity of sound.

Vs = 332m/s + (22-0)oC*0.6m/s/oC
Vs = 332 + 13,2 = 345.2 m/s. @ 22oC.

a. d = Vs*t = 345 * 0.8 = 276 m

b. d1 = d
V*T = Vs*(T+0.8)
3*10^8T = 345(T+0.8)
3*10^8T = 345T+276
3*10^8T = 276
T = 92*10^10^-8 s.

d = V*T = 3*10^8 * 92*10^-8 = 276 m.

To answer these questions, we need to consider the speed of sound and the speed of light.

(a) To find the distance to the explosion without considering the speed of light, we can use the speed of sound. The speed of sound in air at 22.0°C is approximately 343 m/s.

The time taken for sound to travel from the explosion to the physicist is given as 0.800 s. To find the distance, we can use the formula:

Distance = Speed × Time

Distance = 343 m/s × 0.800 s
Distance ≈ 274.4 m

Therefore, the distance to the explosion without considering the speed of light is approximately 274.4 meters.

(b) To find the distance to the explosion by accounting for the speed of light, we need to subtract the time taken for light to reach the physicist from the total time.

The speed of light in a vacuum is approximately 3.00 × 10^8 m/s. However, in air, the speed of light is slightly slower, but for simplicity, we can use the value in a vacuum.

Given that the time for sound is 0.800 s, we can calculate the time for light using the formula:

Time for light = Total time - Time for sound
Time for light = 0.800 s

Now, to calculate the distance considering the speed of light, we can use the speed of light and the time for light:

Distance = Speed × Time

Distance = (3.00 × 10^8 m/s) × (0.800 s)
Distance = 2.40 × 10^8 m

Therefore, the distance to the explosion, taking into account the speed of light, is approximately 2.40 × 10^8 meters.