The speed of light is 3 x 108 m/s. The speed of sound is 343.4 m/s at a temperature of 20°C and 1 atmosphere of air pressure. The speed of sound increases if the temperature increases above 20 and decreases if the temperature decreases below 20. The change is 0.6 m/s per °C. So the equation for the speed of sound when a temperature change is considered is: vs = 343.4 m/s ± (0.6 m/s)(ΔT), where ΔT is the change in temperature. Use the absolute value of the change in T.
Light travels much faster than sound. Seeing the smoke of the starter pistol is almost instantaneous. Hearing the sound of the starter pistol is delayed compared to seeing the smoke. We can use the equation v = d/t to find the time it takes for each wave to reach our senses, eyes and ears.
GIVEN:
d = 800.0 m
T = 15°C, since this temperature is less than 20°C, then (20 - 15 = 5). This means the speed of sound will be slightly slower since the temperature is less than 20.
vs at 15°C = 343.4 m/s - (0.6 m/s/°C)(5°C) = 340.4 m/s this represents our speed of sound at 15°C
c = 3 x 108 m/s = speed of light
v = d/t and t = d/v
UNKNOWN:
t = ? For the sound and the light wave.
SOLUTION:
tlight = (800.0 m / 3 x 108 m/s) = 0.000002667s or 2.667 x 10-6 s. We see the smoke in about 2 millionths of a second from the pistol firing.
tsound = (800.0 m / 340.4 m/s) = 2.350 s. We hear the sound of the pistol firing a little more than 2 seconds after it fires and after seeing the smoke.
