A trombone player stands at the end zone (x = 0) of a football field and begins to play its fundamental tone. Assume the trombone is a half open tube that is 3 m long.
How long does it take, in s, for the sound to travel to the other end zone (x = 300 ft)?
To calculate the time it takes for the sound to travel from one end of the football field to the other, we need to first find the speed of sound.
The speed of sound in dry air at room temperature is approximately 343 meters per second (343 m/s). However, the speed of sound can vary depending on factors such as temperature and humidity. For simplicity, we will assume the speed of sound is 343 m/s.
Now we need to calculate the distance between the two end zones.
The given distance is 300 ft. To convert this into meters, we need to multiply it by the conversion factor of 0.3048 (since 1 ft is equal to 0.3048 m):
300 ft * 0.3048 m/ft = 91.44 m
Therefore, the distance between the two end zones is 91.44 meters.
Now we can calculate the time it takes for the sound to travel this distance. The formula to calculate time is:
Time = Distance / Speed
Time = 91.44 m / 343 m/s ≈ 0.2666 seconds
Therefore, it takes approximately 0.2666 seconds for the sound to travel from one end of the football field to the other.