A sound wave, traveling at 337m/s, is emitted
by the foghorn of a tugboat. An echo is heard
1.76 s later.
How far away is the reflecting object?
Answer in units of m.
To determine the distance to the reflecting object, we can use the speed of sound and the time it takes for the echo to be heard.
The speed of sound is given as 337 m/s. This means that for every second, the sound wave travels a distance of 337 meters.
Given that the echo is heard 1.76 seconds later, we can calculate the total distance traveled by the sound wave. This distance includes the distance from the foghorn to the reflecting object, plus the distance from the reflecting object back to the observer.
The total distance can be calculated using the formula: distance = speed × time. In this case, the distance is twice the distance to the reflecting object because the sound wave has to travel the distance to the object and then back.
Let's calculate the total distance traveled by the sound wave:
Total_distance = speed_of_sound × time
Total_distance = 337 m/s × 1.76 s
Total_distance = 593.12 m
Since the total distance traveled by the sound wave is equal to twice the distance to the reflecting object, we can now determine the distance to the reflecting object by dividing the total distance by 2:
Distance_to_object = Total_distance / 2
Distance_to_object = 593.12 m / 2
Distance_to_object = 296.56 m
Therefore, the reflecting object is approximately 296.56 meters away.