NerdGuy Fridays #13: Speed of Sound

Lightning

Most of us were taught as kids to count seconds after a lightning flash until we heard thunder. Five seconds per mile. This is an okay estimate (5 seconds is actually 1.06 miles at at 20 deg C at sea level), especially as thunder can be a sharp crack or a low rumble that builds and we’re not exactly sure quite when it begins.

Space

In space, sound doesn’t move at all. Think of sound as a shock wave. In space, there’s nothing for it to shock against. (Yes, UberNerds, a sufficiently low frequency note (read as “massive explosion”) would cause ripples through space dust that could propagate across distance over time. For other forms of “shockwave propagation, consider this: https://www.sciencefocus.com/space/can-you-have-a-shock-wave-in-space/.)

The zippy sounds of passing spaceships in Star Trek? Not so much. The sudden shocking silence after a decompression during the first battle in the movie series reboot Star Trek. Cooly awesome!

For now, let’s stick with what we would normally think of as sound.

Earth

When I hit Geology in high school Earth Science, I discovered that sound really does move at different speeds. In fact, I went on to be a Geology major and wrote the first geophysics thesis ever at my school. My research actually covered the study of gravity in projecting subterranean rock formations, but there’s another way to do that.

Sound.

Sound moves at different speeds through different materials. In fact, it can move at 16,000 kmph (10,000 mph) through rock, compared to its lazy meanderings around 1,200 kmph (750 mph in air). What’s more, it travels through different densities of rocks and metals at different speeds.

Much of what we know about the interior of the Earth comes from two sources, earthquakes and atomic bombs. These massive events actually send measurable soundwaves coursing into the Earth’s interior. By a whole series of observations, they have mapped some incredible information. Here’s a textbook chapter on the subject that’s just fascinating.

https://websites.pmc.ucsc.edu/~thorne/TL.pdfs/L_ees.Ch51.pdf

Even if you find this to be a little opaque, there’s a cool map on the fifth page of the pdf (p. 833) of the measured thickness of the Earth’s crust.

Air

But what we typically care about is the speed of sound through air, and in the frequency bands that we can hear. It’s certainly the most useful when I’m trying to place someone in a character’s head in fiction.

So, in my upcoming novel, Ghostrider (Miranda Chase #4) I have someone make this statement.

“…when the world lit up like daylight. I live just back of the airport, two miles from the top of Snowmass, plus a mile down. Counted [xx] seconds before a big boom rolled in—real sharp.”

Calculating that distance should have been easy. A little Pythagorean Theorem of a^2 + b^2 = c^2. That’s a direct line of 2.23 miles from my crash site to my observer. But how long would that take for the sound to travel?

Air at sea level is denser than air at the Aspen Airport at 7,820′ elevation or the top of Snowmass ski area at 12,510′.

Sound moves at 343 m/s (1,125 ft/sec) through air at 20 deg C at sea level. But what is it doing up at Aspen?

Part of that answer lies in this neat little chart:

Speed of Sound at Altitude
Based upon: https://www.centennialofflight.net/essay/Theories_of_Flight/atmosphere/TH1G1.htm as modified for Wikipedia https://commons.wikimedia.org/wiki/File:Comparison_US_standard_atmosphere_1962.svg

At 7,000′ the speed of sound is typically ~312 m/sec. And at 12,500′ is ~295 m/sec.

So, I saw an opportunity to show just what an uber-nerd my heroine Miranda Chase can be. And how she uses that uber-nerdness to determine whether or not to trust someone.

Ghostrider Sound

Brett continued describing the explosion, “I live just back of the airport, two miles from the top of Snowmass, plus a mile down.”

A direct line of two-point-two-three miles—eleven seconds at the speed of sound.

“Counted thirteen seconds before a big boom rolled in—real sharp.”

Thirteen seconds would imply that his distances were inaccurate or his accelerated excitement level at the explosion had caused him to count inaccurately. Assuming he knew the elevation difference between his home and the top of Snowmass mountain, thirteen seconds would place his home two-point-four-five miles horizontally from Snowmass, not two miles.

Though such an inaccuracy seemed unlikely in Brett Vance’s case.

Oh! She’d neglected altitude. The speed of sound slowed in thinner air: nine percent slower at Aspen’s elevation and almost fourteen percent at Snowmass’ peak. If she integrated the speed of sound over the distance, thirteen seconds was surprisingly accurate for a human observer without a stopwatch or other aid.

NERD ON!

NerdGuy Fridays #12: NerdGuy on the Rocks

A Question of Rocks

I recently had the need to look into rock slides for the opening of Miranda Chase #4, Ghostrider. As usual, two simple lines led to a whole field of learning.

“He remained conscious for the next two hundred feet of descent as a [xxx thousand tons of rock swept him toward the valley floor.”…”At the base of the scree slope, the mountain built a [xxx-foot high burial mound.”

Left brackets “[“ are how I note something in my manuscript that I need to look up later but don’t want to stop the flow of writing to do right at that moment. There are other facts that I do have to stop and look up because the answer will affect which direction I take the story. The volume of rock is one of the former kind. But now it was time to unearth the answers.

Weighing Rock

First, how much does rock weigh?

As part of my senior geophysics thesis in college, I had to weigh core sample that we’d drilled out in my field area. Different types of rock have different weights. Think of talc, which is a rock before it’s ground up into a powder, versus a piece of basalt or granite you tossed out of your garden. If you’ve done construction, think of the weight of a sheet of gypsum (another rock) versus a sheet of slate. I can pick up a 4’x8’x1/2” piece of “sheet rock” fairly easily. In my younger days I’d carry them in pairs. I can move a 2’x4’x1/2” piece of slate, if I’m careful and flip it end for end as I go. In my younger days, I may have been stupid enough to lift it, stupid being the operative word.

So, why was I weighing rock? Well, more dense rock also creates a strong gravitational pull. More matter equals more gravity—so denser rock formations under the ground pull down harder. I had the use of a tool called a gravimeter that could measure those minute differences. First I performed a very accurate topological survey. Then a gravimetric survey over the same area. After doing a horrendous amount of math on an incredibly advanced TI-58 programmable calculator that was the envy of my classmates (1977, $125…really dating myself here), I was able to measure the actual variations in the gravimetric field (a whole other topic that I may geek out on someday). I then could computer model (using a program I had to write in BASIC) what was occurring beneath the surface.

TI 58 Calculator
TI 58 Calculator that powered my Geophysics thesis

The Weight of Rock

This is actually much simpler now, plus I required less accuracy for fiction than for geophysics… I used Google.

The very first site I hit included this wonderful information for landscapers.

https://www.hunker.com/12422226/standard-weights-for-crushed-rock-per-meter

  • Solid rock = 2.5 – 3 tons/cubic meter (NerdBonus: a “ton” is 2,000 pounds, a “tonne” is 1,000 kilograms or 2,200 pounds. So we have a mixed English/metric unit here, but I’m going with it rather than converting.)
  • Uniformly crushed rock = 1.6 tons/cubic meter
  • Mixed crushed rock (due to possibly better packing of space) = 1.6 – 2.2 tons/cubic meter
  • Sand and chips (which I don’t care about here, but was interesting) = .92 tons/cubic meter
  • I was very intrigued that all of the following come in the same at 1.07 tons/cubic meter: pea gravel, 1” crushed concrete, recycled asphalt, and 2” sewer filler rock . Pit run gravel (2” or 4”) both weigh in at 1.25 tons (that funny closest-spatial-packing effect evening things out).
  • Landscaping Rock, now we’re talking:
  • 2”-12” rock = 1.25 tons/cubic meter
  • 12-24” rock = 1.18 tons/cubic meter

All right! I’ve walked across scree slopes in the 2”-12” range (not something to do without careful planning and knowledge—neither of which I boasted at the time). I’ve definitely avoided them in the 12-24” category. So, I now have my working weight of 1.25 tons/cubic meter.

How Much Rock

For that I turned to a different website:

https://www.ngi.no/eng/Services/Technical-expertise/Rock-slides

The Norwegian Geotechnical Institute knows a great deal about rock slides. With 174 dead in the last century (most within just 3 events), they have good reason to. A big rock slide in a Norwegian fjord can create town-killing tsunamis. The 2015 movie The Wave is actually a fascinating (and good) movie about this. It’s billed as “Norway’s First Disaster Movie” and earned a nice 6.7 rating on IMDB and 83% on Rotten Tomatoes.

NGI notes that there are actually three distinct categories:

  • Rock fall < 100 cubic meters. This will block a road or train track very nicely.
  • Rock slide = 100-10,000 cubic meters. These only occur on slopes of 50m or more, otherwise there just isn’t enough height to get that much mass moving.
  • Rock flow > 10,000 cubic meters. This caused the devasting tsunamis in 1905, 1934, and 1936.

The scree slopes of the Rockies are truly massive, easily hundreds of meters high in some places and only semi-stable.

How Much Rock

1.25 tons / cubic meter

<10,000 cubic meters (I wanted an event, not a catastrophe.)

These seemed like good working numbers.

So, the first number I wanted was easy: 12,000 tons of rock.

The second was going to take some more thought. How big a mound was created by 10,000 cubic meters?

First I needed to know the natural angle of a scree slope: 32 degrees is typical in the Scottish Cairngorms: http://www.landforms.eu/cairngorms/scree.htm. Close enough for me. My final cone had to have a radius 3 times wider than it was high.

My search for “Calculating the Volume of a Cone” brought up a neat tool right away.

I fooled around with some numbers until I got this result:

Volume of a Cone
Volume of a Cone

Thirty meters wide and ten meters high didn’t sound very impressive as a burial mound. But then I thought about it. 1) That’s a radius of 30 meters, so a diameter of 60 meters. 2) It’s in metric.

English is always better for measurements like this. A burial mound that was 200’ across and 30’ high—way better.

But was there a better descriptor? I started tinkering.

  • A circular base 200’ in diameter = 31,400 square feet.
  • A football field = 47,970 square feet without the endzones. (“Covering two-thirds of a football field…” sounds a little lame.
  • A FIFA soccer field is even bigger, so that wouldn’t help.
  • From my on-going US Coast Guard short story series, I know that an Endurance-class cutter is 215’ long. But that’s long and narrow, so it doesn’t give the right impression.
  • A US Interstate Highway uses a 12’ lane. 200’/12’ = 16 lanes. Hmmm…

Another NerdBonus: according to Quora, the widest highway section in the US Interstate system runs for 22 miles from Katy, TX to Houston, TX. It averages 22 lanes wide and in some places is 26! Excluding toll booths, it’s the widest in the world. (With tollbooths, it’s 50 lanes on the G4 in China.)

But most of us don’t have much experience with picturing a 16-lane highway. I needed something familiar to most people.

  • A baseball field = 400’ x 400’ = 160,000 sq feet. Nope.
  • A baseball infield = 90’ x 90’ = 8,100 sq feet. Closer. Though if you start looking at specifications for the infield and the dirt running track you find out that: 1) maybe 27,000 is a workable number, but 2) there aren’t actually specific rules according to the blogs on mlb.com. So picturing something that’s variable…nah!

“He remained conscious for the next two hundred feet of descent as a eleven-and-a-half thousand tons of rock swept him toward the valley floor.”…”At the base of the scree slope, the mountain built a burial mound—bigger than a baseball diamond but smaller than the dirt running track and three stories high.” Not really helpful. Even without the running track qualifier it seemed clunky.

  • A full-sized school bus is 45’ long. Hmmm…

“He remained conscious for the next two hundred feet of descent as a eleven-and-a-half thousand tons of rock swept him toward the valley floor.”…”At the base of the scree slope, the mountain built a burial mound—wider than four school buses parked end to end and three stories high.”

Yeah, there it is.

UberNerd Note: Yes, I considered the fact that the mound wouldn’t be accumulating on a perfectly flat valley floor, but rather at the foot of the existing 32-degree(ish) scree slope. But I couldn’t think of how doing all that extra math would make these 2 lines in the book any more impactful—rather quite the opposite, so I left truncated cones and other calcs for a different time.

Until next time: Nerd on!