You are viewing a New Year's Day fireworks display at a distance of 1500 m. It is 4.0°C. How long does it take the sound of the fireworks exploding to reach you?
time=distance/velocitysound
so figure the velocity of sound at 4C
i got 375 seconds but that was wrong. what do divide 1500 by 4?
To determine how long it takes for the sound of the fireworks exploding to reach you, we can use the speed of sound formula. The speed of sound can be approximated as 343 meters per second at normal atmospheric conditions, such as a temperature of 20°C. However, since the temperature is given as 4.0°C, we need to account for the temperature difference.
The speed of sound is affected by temperature because sound travels faster in warmer air and slower in cooler air. To calculate the adjusted speed of sound, we can use the formula:
v = v0 * √(T/T0)
where v is the adjusted speed of sound, v0 is the speed of sound at a reference temperature (usually 20°C), T is the current temperature, and T0 is the reference temperature.
Let's plug in the values:
v0 = 343 m/s (speed of sound at 20°C)
T = 4.0°C (current temperature)
Using the formula, we have:
v = 343 * √(4.0/20)
v = 343 * √(0.2)
v ≈ 343 * 0.447
v ≈ 153.621 m/s
Now that we have the adjusted speed of sound, we can calculate the time it takes for the sound to travel the distance of 1500 meters. The formula for time is:
time = distance / speed
Plugging in the values:
time = 1500 m / 153.621 m/s
time ≈ 9.76 seconds
Therefore, it would take approximately 9.76 seconds for the sound of the fireworks exploding to reach you.