I'm going to remove speed (speed = 1) and make the distance unitless.]]>

Okay, let me know what you need to solve it.

]]>Let me work that through a few times.

Thanks.]]>

This can be solved easily and is very similar to your problem:

Q: Four listening posts are stationed in the Pacific 1000 miles apart at A,B,C and D. They form a 1000 mile square. A nuclear explosion of unknown origin is detonated inside the square. The sound detectors are very sensitive and pickup the sounds according to this data

C gets the sound at 3:00 am exactly.

D gets the sound 28.707489170445314 minutes later.

B gets the sound 38.581659920734374 minutes later.

A gets the sound 54.87964482242969 minutes later.

The speed of sound was given as 768 mph.

Where in the square does the explosion occur and when?

The equations become:

x1 = 700

y1 = 800

distc = 360.55512754634225 miles

It is now easy to answer the remaining question.

]]>I have solved a problem like this using two methods. One is an iterative approach and the other requires solving a 3 x 3 set of equations all of which are circles.

]]>http://math.stackexchange.com/questions … angulation

But you need a maths package to solve the equations.

I don't think there is a way to post a spreadsheet. I take screen shots and post the resulting images.

Bob

]]>```
x y tB tC tD tA
4 4 10.84 16.97 10.84 0.00
4 8 3.70 11.06 8.94 0.00
8 4 8.94 11.06 3.70 0.00
8 8 3.11 5.66 3.11 0.00
3 12 0.00 10.24 12.26 3.83
3 16 0.00 12.46 18.35 11.28
6 18 0.00 7.82 16.48 12.65
9 12 0.00 1.56 4.24 2.96
9 16 0.00 1.86 9.57 8.51
10 10 0.00 0.00 0.00 0.00
11 2 11.88 10.91 0.00 1.96
14 5 12.71 8.35 0.00 7.06
16 3 18.35 12.46 0.00 11.28
17 2 21.15 14.64 0.00 13.51
18 6 16.48 7.82 0.00 12.65
14 14 6.75 0.00 6.75 11.31
14 18 7.82 0.00 12.65 16.48
16 16 10.84 0.00 10.84 16.97
18 14 12.65 0.00 7.82 16.48
18 18 15.28 0.00 15.28 22.63
```

Oh, just to help, I changed it to a 20x20 universe instead of 10x10. :-(

]]>I've hit an algebraic barrier, and, so far, cannot get round it.

Let sound be at time T, and the times at the points be Ta, Tb etc. Speed of sound, s. Then

From which T can be eliminated thus:

Trouble is there are 5 unknowns and only 4 equations.

I'm wondering if there is a way to compute these by trial and improvement.

Anyway, I haven't stopped thinking ........................

Bob

]]>Welcome to the forum!

Of course it is worthy. But that doesn't mean we can do it. I'm still working on a problem set over two years ago. I'll start thinking about it. Meanwhile, someone else will probably nip in and provide a solution.

Back later.

Bob

]]>First post. Hope it's worthy.

I need to calculate the position in 2D space of an "event" using four sensors positioned at the corners of the rectangular "universe".

Let's say the event is a sound which might occur somewhere inside the rectangle and the sensors are microphones.

Is it possible to calculate the co-ordinates for the epicentre based on the time for the sound to reach each of the four sensors?

At first sight, it seems straightforward enough. Until you realise that you don't know what time the event happened at, so you don't actually know the time for the event to travel to any of the sensors. You only know the time delta between the sound hitting each of the sensors.

So, the event happens at time S (but we don't know when that was). Then (in the shown example) the soundwave hits B A C and D. We can see that the timestamp registered at point C is going to be the time SC minus the time SB, etc:

tC = SC - SB and

tD = SD - SB

tA = SA - SB

But we don't know time SB.

Can anyone help me find the location of S, please?

Rules suggest I should indicate my "level". Well, I didn't sit high school maths, but I'm a masters degree qualified Aerospace engineer. So, I'm a bit irked that I couldn't work this one out for myself...

]]>