Squares

General FreeBASIC programming questions.
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

With guitar strings:

The strings press down pretty easy.. So they are like several times harder than water.

So the 23 meters a second , speed of waves in water.. Would be multiplied several times.

But different guitars have different "Scale Lengths" : the distance from the bridge to the neck bar...
https://guitargearfinder.com/guides/ult ... le-length/

In a standard size guitar "24 inch" , the "A" string is 440 Hz..
I'm not sure how to break that down into meters a second.. per hardness..

Two feet is 0.6096 meters..
23 meters a second \ .6096 = 37.729658793 meters a second , times the hardness? = ??
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

Two feet is 0.6096 meters..

23 meters a second \ .6096 = 37.729658793 ; the wave would propagate the strings at 37.729 times a second (37.729 Hz)

Since the guitar "A" string is 440 Hz , then the hardness of the guitar "A" must be just over 10 times the hardness of water.
10 times would 377.29 Hz

11.662 times the hardness of water, would be 440 Hz

Exposing the strings to a speaker pulsing at 37.729 times a second , should make all the strings , ring in their frequency..
Mistake: ( You have to wait for the wave to travel , out and back) So it would be half = 18.8645 pulses a second , to make the strings ring.
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

You take the speed of waves in water ; 23 meters a second ,
And divide that by the meter diameter of the object you want to earth quake.
And then multiply it by the hardness...

For a 23 meter wide building , the waves , would propagate that distance in water , at once a second..
If concrete is 100 times harder than water.
Then 100 Hz should make the building earth quake.. Since you have to wait for the waves to go out and back , it would be 50 Hz ( half )

I think its lower than that , that seem to be a little high...

( Tesla's Earth Quake Machine ) was either a an electric solenoid or pneumatic tamper..
I don't think solenoids , can pulse more than a few times a second..
I don't think you could get one doing 100 pulses a second..
A pneumatic tamper can pulse at higher rates.
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

In my experience , with the steel rail...
It was 3 feet high and 4 feet long.. 2 inch wide tubular steel , 1/4 inch thick.

So you could figure it to be the same as a guitar string.. 3 + 3 + 4 = 10 feet long.

I was tapping it less than twice a second.. and it was wobbling like rubber. nearly a foot in each direction..
It was swaying back and forth and every time it came back , i tapped it again , with the side of my fist , and the waving kept getting bigger.

I found out by trail and error , that if you tapped it at a certain time , it would stop waving or go into harmonics and vibrate.

And i thought: "That's how Tesla's earth quake machine works. " ( Waveform Amplification )

It works like a playground swing , except there's no gravity to slow it down..
So every time the swing comes back and you push it , it swings out further each time.

With the playground swing:
If you push the swing at 5 pounds of force, it will swing like 2 feet.
If you push the swing at 50 pounds of force , it will swing like 5 feet.

In the waveform world:
You push the swing at 5 pounds of force , and it will swing 2 feet
if you push it a second time , at 5 pounds of force , it will swing 4 feet. The same force keeps amplifying the waveform.
( if you push it harder , naturally it will swing higher.)
But just a methodic pushing at the same force , will make the swing swing higher each time.

The waveform is the playground swing.
You pulse the building and wait for the wave to come back , and then pulse it again..
The wave will get bigger each time you pulse it in time with the wave. ( swing coming back. )

As the waves get bigger ( swing swings further ) you might have to slow down the pulsing to coincide with the wave???
Tesl'a machine had a gear in it... Maybe that gear slowed the pulses to put it in time with the bigger waves??
dkr
Posts: 37
Joined: Nov 20, 2015 15:17
Location: Alabama, USA

Re: Squares

Albert,
You are not considering damping in any of these systems. Small displacement usually have linear damping. However, as the displacement increases the damping usually increases non-linearly i.e. increases rapidly. Otherwise, many structural systems would be failing with small inputs at the fundamental structural modes. Most systems have significant amounts of damping. You need to get a decent structural dynamics textbooks to understand these concepts.

Good Luck!

Darren
Richard
Posts: 3027
Joined: Jan 15, 2007 20:44
Location: Australia

Re: Squares

It is at times like this that I listen to Marc Abrahams performance at the recent Ig Noble Prize awards.
You can watch it here; https://www.youtube.com/watch?v=BdnH19KsVVc
Or via https://www.improbable.com/tag/dunning-kruger/
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

For the steel rail i was playing with.. 10 feet ( 3 feet high by 4 feet long , 3+3+4- =10 feet )

10 feet is 3.048 meters

23 meters a second / 3.048 = 7.666 traverses a second... ( half would be 3.833 times a second, ) 1/4 second intervals...

I think i was tapping it , a little slower than that...
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

@Richard

The Tacoma Narrows Bridge..

Design Suspension
Total length 5,939 feet (1,810.2 m)
Longest span 2,800 feet (853.4 m)

23 meters a second / 853.4 = 0.026951019 traverses a second ( half = 0.01347551 ) = 1 pulses every 134 seconds
Then you mul that by the hardness , maybe 100?? = 1.34 pulses a second.. ( that's about the normal wind gust. )

If you put a plastic film on water , and push it down = the force it takes to push down , would be hardness 1
A concrete bridge span , would be like 100 times harder to push down . than water. So it would be like hardness 100..

So ; for the hardness , you calculate the force it takes to flex the object.
A length of rebar , is pretty easy to flex..
So its only a few times harder than water , even though it's made of steel which is actually hundreds of times harder than water..

A block of cement, you tap it with a hammer , and waves go through it,
( The wave is a flex , it flexes with hardly any force. ) So concrete is only a few times harder than water.
That's why i was thinking ; that propagation waves , traverse all substances at the same rate. The rate of waves in water...
albert
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Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

A 10 feet length of 1/2 inch rebar, flexes pretty easy , just a few pounds to make it flex.
A 1 foot length of 1/2 inch rebar , takes several hundred pounds of force , to make it flex. So you would pulse it at a higher frequency.

Same with concrete:
A 100 foot span flexes pretty easy. While a i foot span takes much more force.

You take the speed of waves in water ; 23 meters a second ,
And divide that by the meter diameter of the object you want to earth quake.
And then multiply it by the hardness... ( how much harder it is to flex it , than water. )
dodicat
Posts: 6552
Joined: Jan 10, 2006 20:30
Location: Scotland

Re: Squares

I was going to say that the Moh's hardness scale only applies to solids, but I see mercury documented as hardness 1.5.
The other liquid element at room temperature is bromine, but it is not listed.
jj2007
Posts: 1523
Joined: Oct 23, 2016 15:28
Location: Roma, Italia
Contact:

Re: Squares

dodicat wrote:I was going to say that the Moh's hardness scale only applies to solids, but I see mercury documented as hardness 1.5.
The other liquid element at room temperature is bromine, but it is not listed.
The Mohs value for mercury is valid only for solid mercury at -38.89 Celsius grades and lower.
dodicat
Posts: 6552
Joined: Jan 10, 2006 20:30
Location: Scotland

Re: Squares

I guess you are correct jj2007.
I was looking at
https://en.wikipedia.org/wiki/Hardnesses_of_the_elements_(data_page)
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

I think if you took a diamond rod , 100 meters long.. It might flex , pretty easy.. like rebar??

So: as you cut the length in half , that should make the hardness double..

Each time you cut the length in half the hardness doubles up?

So it should be that a ten foot length of rebar , flexes at half the weight as a 5 foot length.
Every time you cut the length in half the hardness doubles.

A 10 foot length of rebar , flexes at 10 pounds.
A 5 foot length of rebar , flexes at 20 pounds. ?? might be higher??
Maybe the 5 foot length would require 100 pounds to make it flex??

The hardness might go up exponentially with halfs??
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

@dkr

You mentioned damping....

Like a playground swing:
If you stop pushing it ; it will eventually stop swinging.. Gravity and air resistance causes the swing to gradually slow down.

In the waveform world you don't have air resistance. So only gravity counts.

When you pluck a guitar string it will vibrate for several seconds..Breaking into higher and higher harmonics.
Maybe gravity , then plays a role , to slow the waves?
Maybe the harmonics , gradually cancel out the waves , till it stops vibrating?

Maybe the gravity pulling down through the object, affects the waves ability to propagate?
So; there might be such a thing , as gravitational damping?
albert
Posts: 5709
Joined: Sep 28, 2006 2:41
Location: California, USA

Re: Squares

Living in California , where we have a lot of earth quakes.

When an earth quake strikes , the mountains vibrate and shake , the sands and soils in the valleys , undulate like crazy..

So the earth quake , makes sand and soil move a lot more than bedrock.

The softer the substance , the bigger the earth quake waves.