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 away(m) is the explosion if air temperature is 22.0°C, neglecting the time taken for light to reach the physicist?
(b) How much further away(m) would the explosion be calculated to be if the speed of light is taken into account?
See 5:58 PM post.
To find the distance to the explosion, we can use the speed of sound in air and the time lag between seeing the explosion and hearing its sound.
(a) Neglecting the time taken for light to reach the physicist:
The speed of sound in air at 22.0°C is approximately 343 meters per second.
d = v * t
where d is the distance, v is the velocity, and t is the time.
We can solve for d by plug in the given values:
d = 343 m/s * 0.800 s
d ≈ 274.4 meters
So, the explosion is approximately 274.4 meters away.
(b) Taking the speed of light into account:
The speed of light in a vacuum is approximately 299,792,458 meters per second.
Since the time taken for light to reach the physicist is negligible compared to the time lag between seeing the explosion and hearing its sound, we can assume that the light reaches the physicist instantaneously.
To calculate the distance taking the speed of light into account, we need to find the time it takes for light to travel the same distance as sound.
The time taken for light to travel the distance can be found using the equation:
t = d / c
where t is the time, d is the distance, and c is the speed of light.
Plugging in the values:
t = 274.4 m / 299,792,458 m/s
t ≈ 9.15 × 10^(-7) seconds
Therefore, the explosion would be calculated to be approximately 9.15 × 10^(-7) seconds further away when taking the speed of light into account.
Please note that this value is extremely small and practically negligible for most real-world scenarios.