You and a friend are sitting in the bleachers of a major league baseball park, 1
ID: 2259564 • Letter: Y
Question
You and a friend are sitting in the bleachers of a major league baseball park, 103 m from home plate on a day when the temperature is 20° C. Your friend is listening to the radio commentary with headphones while watching. The broadcast network has a microphone located 17 m from home plate to pick up the sound as the bat hits the ball. This sound is transferred as an EM wave a distance of 79,000 km by satellite from the ball park to the radio.
(a) When the batter hits a hard line drive, who will hear the "crack" of the bat first, you or your friend?
What is the shortest time interval between the bat hitting the ball and one of you hearing the sound?
(b) How much later does the other person hear the sound?
I found part a to be 0.29985 s but I can't get part b. I already tried .01315 and .03635.
Explanation / Answer
first the person without the headphones will hear the sound in a time of
time = distance/speed of sound = 103m/343m/s = 0.2998s
the sound heard by the person listening to radio will travel as a sound wave 17m to the microphone, then make a round trip of 79,000 km as a radio wave traveling at the speed of light
the time for this trip is
time = (17m/343m/s) + (79,000km/300,000km/s)
= 0.0496s+0.264s = 0.3136s
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