Question

You and your family are attending an annual 4th of July fireworks display. During the show, you observe that the sound from the exploding fireworks arrives 2.5 seconds after the light from the explosions. Knowing that the air temperature that night was 26°C, determine the distance (in meters) between you and the fireworks.

Round to the nearest whole number.

Technical Note: The setup for this problem assumes that the sound from the exploding firework takes time to reach you (on the order of a second) but that you see the explosion without a time delay. This is an oversimplification! However, light travels really, really fast (about 300,000,000 m/s). The light travel time at a fireworks show is on the order of millionths of a second, so for the purposes of this problem it is OK to approximate that you are seeing the fireworks without a time delay.

Please show all work!

Answer 1

Answer: The speed of sound in air depends on temperature, pressure, and humidity. For dry air at 26°C, the speed of sound is approximately 346 meters per second.

Let's call the distance between you and the fireworks "d". We can use the fact that the time it takes for the sound to reach you is 2.5 seconds longer than the time it takes for the light to reach you:

d = speed of sound x time delay

d = 346 m/s x 2.5 s

d = 865 meters

Therefore, the distance between you and the fireworks is approximately 865 meters.