Fellow Science Lovers,
Gaming update: No updates this time. I’m absorbed with writing and revising Scribes Emerge.
What is an Echo?
In Scribes’ Descent, why is there a mention of some rooms echoing and not others? To answer this, let’s take a closer look at sound. Or perhaps a closer listen. 
An echo is reflected sound. Unless the walls are lined with foam, all rooms reflect sound. So if that’s true, why don’t we hear echoes all the time? Answer: most rooms are too small. Without enough delay, the original sound and the reflected sound are so close together that the human ear can’t tell them apart. Let’s do some math to see just how big a room must be to make an echo:
The needed delay is around 1/10 of a second. Sound travels 112.5 ft in that time.
Speed of sound in air at 20°C = 343m/s or 1,125.33 ft/s.
1,125.33ft/10 = 112.5 ft
That’s a minimum of 112.5 ft of total distance. Divide that by half (assuming a sound wave travels to the wall and returns along the same path). That gives you 56.3 feet or 17.1 meters. That’s how long the longest side of the room must be in order to hear an echo.
But wait. Didn’t Mallory hear echoes in a tiny chamber in the the Garden of Bones? “Loud snorts and growls echoed in the cramped chamber.”
What was that referring to?
What Mallory was hearing wasn’t echoes, but reverberations. These happen when sound takes < 0.1s to return to the listener. In that case, the original and reflected sound waves are so close together that the brain perceives them as a single, continuous sound. This is what Mallory heard in that tiny stone chamber. (Its close, parallel surfaces cause sound waves to bounce back and forth a lot with little losses though the air compared to a larger space: https://www.fellert.com/blog/interestingfacts/reverberation-…)
Watch this video for a demonstration of echoes and reverberations in sound editing software: https://www.youtube.com/watch?v=LR-AYApQbNE
Factors Affecting Echoes and Reverb
Distance isn’t the only consideration. The composition and temperature of the air and the absorptive quality and number of the reflecting surfaces also matter. Intuition tells us that filling a room with more objects–especially soft ones–greatly reduces echo and reverb. Air temperature’s impact, however, may not be so obvious.
Colder air requires less distance to create echoes because it slows down sound waves. Why is this? Well, the molecules in colder air move more slowly, so they carry sound waves more slowly, too. By dropping the temperature by 1°C, the speed of sound drops by around 0.17%. You can calculate the speed of sound in air with this formula:
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Here, T is the air temperature in Celsius, which will cancel out with the C in the denominator in the second term. Sound in a room that is -50°F or -45°C will travel at 302.35m/s. (I used this online calculator: https://www.weather.gov/epz/wxcalc_speedofsound) Dividing that by 10 gives you 30.2m or 99ft. Dividing this by 2 to account for the return path gives you 15m or 49.5ft. Compare this with the previous calculation at 20°C, which was 56ft. The colder room can be almost 6.5ft narrower and still make an echo. The cold also stiffens all materials in a room, making them harder and more reflective.
References:
https://senix.com/ultrasonic-sensor-accuracy/
https://www.scienceabc.com/humans/why-cant-echoes-be-heard-i…
https://www.nde-ed.org/Physics/Sound/tempandspeed.xhtml
https://en.wikipedia.org/wiki/Reverberation
For those jonesing for more math goodness, the Sabine equation and the Eyring equation give a good estimation of reverb time. Here is a sound absorption coefficient vs frequency chart to help you plug values into those formulas:
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And here’s an article on how to run the calculations: https://www.engineeringtoolbox.com/accoustic-sound-absorptio…
Now you know how to build a room that echoes, which I’m sure everyone has on their todo list, right?
Have any questions for me about anything in the Scribes Series or Emolecipation? Reply to this email and let me know!
Writing update: So far, I’ve rewritten the first 40 chapters of Scribes Emerge, Scribes Series book 3. This one is shaping up to be quite a bit longer that the first two books.
See you next month,
Dylan West
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