Sound on Refuge

When I created Refuge in my mind, I created a world much larger than Earth.  A world that while much greater in ocean coverage percentage wise, still has three times the land area of Earth.  That’s a lot of breathing room!

I’m writing what is currently Chapter 19, and there is an explosion.  I’m telling the chapter from the point of view of someone who is about as far away form the city as you would ride in a shortnight, so no longer than 99 minutes (see earlier blog about the day/night cycle).  At 6kph, that’s about 9 kilometers.  So I need to calculate how long the sound from the explosion would take to reach the viewer.

It’s not as simply as it sounds.  On Earth the speed of sound is 343mps, roughly, but it will be different on Refuge because the atmosphere is, I’ve decided arbitrarily, about 1.5 times as dense as Earth.  Why did I decide this?  Mainly because of two reasons.  The first is that Refuge has 1.16x the gravity of Earth, so it is likely to retain more.  But Refuge is also inside of a gas giant moon system.  Not just inside, but one of the inner moons.  The density of stray matter near that planet (it’s 11 times Jupiter’s mass) is going to be higher and Refuge would have picked up more gasses in the first place.

While searching for my answer to see how much faster/slower sound would travel on Refuge, I came to this page:

http://www.newton.dep.anl.gov/askasci/phy00/phy00999.htm


I mention this often, but I’m not a physicist.  My eyes, however, are drawn to this formula:

For sound propagating through a gas, the speed is given by

v = sqrt (B/u) where B is the bulk modulus B = – dp/(dV/V).
For air, B = 1E5 N/m^2 (for a gas, B = the pressure) and u = 1.3 kg./m^3 giving v=277 m/s.

I’m fairly sure, since U=density, that I can simply multiply 343mps by 1.5 and roughly arrive at my conclusion.  I don’t need precise numbers, since the person I’m writing the POV from is pre-high tech and not wearing a watch.  It’s not like she’s going to say, “The sound took 18.2 seconds to reach me.”

But I do need to know if it’s slower, or faster, and give a general idea of the delay.  The reason the result above doesn’t reach the correct result is that because sound traveling in air doesn’t transfer heat, which increases the bulk modulus (B) in the formula above.  

I am not going to learn about that in detail, but consider that sound on Refuge travels roughly 1.5 x 343mps, or roughly half a kilometer per second.

9 kilometers outside the city, for purposes of my book, Merik hears an explosion 18 seconds (or in her estimation, four breaths) after she sees it.