Two fans are watching a baseball game from different positions. One fan is located directly behind home plate, 18.3 m from the batter. The other fan is located in the centerfield bleachers, 127 m from the batter. Both fans observe the batter strike the ball at the same time (because the speed of light is about a million times faster than that of sound), but the fan behind home plate hears the sound first. What is the time difference between hearing the sound at the two locations? Use 345 m/s as the speed of sound.
A)0.316 s
B)0.368 s
C)3.17 s
D)1.89 s
E)0.053 s

Question

Quizplus · Accepted Answer

We can use the formula:

distance = speed x time

to find the time difference between the two locations. Let's call the time difference "t".

For the fan behind home plate:

distance = speed x time 
18.3 m = 345 m/s x t

Solving for t:

t = 18.3 m / 345 m/s 
t = 0.053 s

For the fan in the centerfield bleachers:

distance = speed x time 
127 m = 345 m/s x (t + X)

where "X" is the additional time it takes for the sound wave to travel the extra distance from home plate to centerfield.

Solving for X:

X = (127 m) / (345 m/s)
X = 0.368 s

Therefore, the time difference between hearing the sound at the two locations is:

t + X = 0.053 s + 0.368 s = 0.421 s - 0.053 s = 0.316 s

So the answer is A) 0.316 s.

Two Fans Are Watching a Baseball Game from Different Positions