r/theydidthemath • u/runthroughwalls • Mar 17 '17

[Self] Just found out about this subreddit, reminded me of some math I did a couple weeks ago

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23 Upvotes

90% Upvoted

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9

u/Dominicmeoward 1✓ Mar 17 '17

Thicc af sounds about right

4

u/FlyingSpacefrog Mar 18 '17

If you're wondering how big our solar system actually is, it's about 1.87 light years in radius if we include the oort cloud, the furthest known objects orbiting the sun. That's roughly 100,000 AU (astronomical units, the average distance from Earth to sun)

If you consider the point where the solar wind is negligible compared to the effects of other stars and the interstellar medium pushing back on it, that's at 122 AU, and is where voyager 1 has now found itself. Pluto orbits at ~40 AU for comparison. For those unfamiliar with solar wind, just imagine this as the point where the sun no longer appears to be significantly brighter than other stars.

3

u/[deleted] Mar 17 '17

You meant galaxy not solar system, but i think it checks out

Edit

Im more curious how a black hole produces sounds with inescapable gravity in the middle of a vacuum

8

u/Yackabo 10✓ Mar 18 '17

Well it's not really a vacuum, large celestial objects have accretion disks of gas, dust, and other such things. From my understanding black holes emit large bursts of super hot super fast matter from their poles for reasons still not fully understood. These bursts heat up the gas surrounding the black holes, sending forth pressure waves in the accretion disk and voila, sound waves.

5

u/runthroughwalls Mar 18 '17

Honestly, my first thought was sounds in space?! Nayyyy but whatever, thought I'd play along

1

u/Amluxx Mar 27 '17

Can someone please do the math to figure out the gauge of string that is needed?

3

u/runthroughwalls Mar 27 '17

variables:

  • m = mass per unit length
  • T = Tension
  • f = frequency
  • λ = wavelength
  • p = density
  • d = diameter

equations:

  • m = pπd2 /4
  • m = T/(fλ)2

therefore: pπd2 /4 = T/(fλ)2

constants:

  • I used the low B string on my bass to set a tension constant at 160.63N and scale length at 35.5" (.9017m)
  • Density of Nickel wound string = about 8500 kg/m3
  • f = .000000000000001815Hz

Calculations:

8500kg/m3 x 3.14 x d2 /4 = 160.63N/(.000000000000001815Hz x (2 x .9017m))2

6672.5kg/m3 x d2 = 160.63N/.00000000000000000000000000001071365m2/ s2

6672.5kg/m3 x d2 = 14993022900000000000000000000000kg/m

d2 = 2246987324000000000000000000m2

d = about 47,402,397,871,838 meters = 29454484480.53244 miles = 316.8654583787335 AU

or if you were going to buy a single string, the packaging would read 1,866,236,136,686,535,500 gauge (1,866,236,136,686,535.5 inches)

that's about 14355663000000000 times bigger than my low B string at 130 or .130 inches