David is in a large stadium listening to the first words form the
astronauts who have landed on Europa. David is 80 meters from the loud
speaker. The radio station which is broadcasting the message from
Europa is 100 km from the stadium.
Assuming that Europa is at its ?average? possible position from Earth,
how long will it take the sound from the astronaut?s mouth to reach
David?s ears?
Hello kim2, I noticed that no one had actually answered your question
and felt that we owed you an answer. Here is some info you need to
find your answer:
Speed of light: 300,000 kilometers per second in a vacuum
http://www.school-for-champions.com/science/lightspeed.htm
Speed of sound (since you don't specify we will assume these conditions):
In air at sea level, 60% humidity and 30 C, it is 344 meters per second.
http://www.sizes.com/natural/sound.htm
Distance from Earth to Jupiter:
Minimum 588.5 x 10^6 kilometers
Maximum 968.1 x 10^6 kilometers
http://www.the-planet-jupiter.com/jupiter-fact-sheet.html
Distance from Jupiter to Europa: mean distance 670,900 km
http://www.enchantedlearning.com/subjects/astronomy/planets/jupiter/moons.shtml
Using the above info plus what you give in your question we can
calculate the answer:
Time for light/radio signal to travel from Jupiter to Earth:
Maximum = 968.1 x 10^6 kilometers/300,000 kilometers per second = 3227 sec.
Minimum = 588.5 x 10^6 kilometers/300,000 kilometers per second = 1962 sec.
NOTE: This agrees with the comment made by iang-ga.
Time for light/radio signal to travel from the radio station to the
receiver at the stadium:
Time = 100 kilometers/300,000 kilometers per second = .003 sec.
Time for sound to travel from the speaker to David's ear:
Time = 80 meters/344 meters per second = .23 sec.
Now we have to decide exactly how accurate you want your answer to be.
If you want to consider that the astronauts are actually on Europa and
not Jupiter, you will introduce another variable. Since the mean
distance from Europa to Jupiter is 670,900 km we would have to include
this in our calculations.
Time = 670,900 km/300,000 kilometers per second = 2.24 sec.
To get an exact number we would have to know the exact relationship of
Europa's orbit to Earth's which is a subject I don't want to tackle.
So, we will just assume that the astronauts sent their message from
Jupiter.
Then we have two answers, one maximum and one minimum.
Maximum = 3227 + .003 + .23 = 3227.233 sec.
Minimum = 1962 + .003 + .23 = 1962.233 sec.
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speed of sound