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 Subject: speed of sound Category: Science Asked by: kim2-ga List Price: \$5.00 Posted: 28 Nov 2004 22:35 PST Expires: 28 Dec 2004 22:35 PST Question ID: 435394
 ```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?```
 Subject: Re: speed of sound Answered By: redhoss-ga on 30 Nov 2004 09:14 PST
 ```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. I hope that this is what you were looking for, Redhoss```
 ```Europa to loud speaker: speed of light * distance between loud speaker and Europa + loud speaker to ear: speed of sound * 80 meters = length of time right?```
 ```Time = Distance / Speed You can for all practical puposes ignore the time taken from Europa to Stadium as the time would be negligible (Speed of light = 3 X 10^8 m/s) Thus, in our case Time = 80 / 340 = 0.235 seconds (Speed of Sound = 340 m/s)```
 ```The maximum light travel time from Europa is 54 minutes and the minimum is 33 minutes - not exactly negligible :-) Ian G.```
 ```There is a problem with the answer: the accuracy of the answer (to within a thousandth of a second) is totally inappropriate given the inaccuracy of several of the variables. The most-rounded variable is the figure used for the speed of light: a straight 300,000 Km/sec. (the speed of light is actually 299 792 458 m/s) The figures used for distance to Jupiter are to the nearest hundred thousand kilometers (possibly that is as accurate as we can measure them). In science, one should never present an answer to a higher degree of accuracy than the input variables support. Round the answers off accordingly. -Lep```