Time Delay

Have you ever noticed that there is a time delay between when you see a firework and when you actually hear the same firework?

To explain why we can observe a detectable time delay between the light and sound of fireworks, remember that at normal atmospheric pressure and a temperature of 15^oC, sound waves travel at 341 m/s. While this speed may seem fast, the speed of a sound wave is slow in comparison to the speed of a light wave which travels at approximately 300 000 000 m/s, nearly 900 000 times the speed of sound!

The arrival of the light wave from the location of the firework detonation occurs in so little time that it is essentially negligible. The arrival of the sound wave from the location of the detonation however occurs much later in comparison to the light wave. The time delay between the arrival of the light wave and the arrival of the sound wave can allow a person to approximate their distance from a firework.

Also remember that: Distance = velocity x time or D = vt

Another interesting fact is that the further you are from the firework, the harder your brain tries to compensate for the time delay between the sound and light. Scientific studies have concluded that your brain will actually think that the time delay is less than it actually is in an effort to try to reduce the time delay difference. “The brain coordinates the auditory and visual input, so that no delay is noticed even though the sound arrives later.” (Nature 421, 911 (2003) ) The graph below shows the results of one of these studies.

Question #1

A spectator watches the fireworks finale on a breezy August night with a temperature of 15^oC. Their seat at on the beach at English Bay is at a distance of 250m from the Symphony of Fire barge. They see a large blue and red firework at an angle of 45^o from the horizontal. Calculate the time delay between when the observer sees this firework and when they hear the same firework. (Hint: The delay of the light is negligible compared to the delay of the sound. Also remember that the distance from the barge is different than the distance from the firework.)

Question #2

On August 3^rd, a science and math student from U.B.C. went to English Bay to watch the fireworks finale. Two of her friends were disagreeing on how far the barge was from their seat on the hill. Mike, an engineer, said it was 200m, while Gregg, a businessman, said the distance was more like 1km.

The U.B.C. decided to resolve their conflict, and took measurements of the approximate angle of the fireworks, which she found to be 65 o. She then took a stopwatch and timed the delay time between when she saw the firework, and when she heard the firework. She concluded that the time delay for the fireworks at this height was 1.70 sec.