The point has been made, but "dimensions" is a general concept that can apply to anything. Number of variables = number of dimensions. What each dimension (variable) represents can be assigned to anything you choose.
Spatial dimensions are but one example. For spatial dimensions, each...
The spatial dimensions are orthogonal and fundamentally independent. I don't see time as being analogous. If you had 5 spatial dimensions, they could all independently vary in time.
Regarding "enveloping", I have similar philosophical musings, that moving in time is somehow perpendicular to...
The Fourier coefficients can be plotted, giving you the frequency domain expression for the waveform. A spectrum analyzer.
Fourier transforms (and FFT, DFT, etc) transform waveforms between the time and frequency domain. Defining the frequency response of a filter in the frequency domain, for...
Saying that the force equals the mass times the acceleration provides an identity that allows you to understand the very real relationship between force mass and acceleration. Now, you can say it is misleading because I measured the mass yesterday and the acceleration today and it didn't give...
It is an averaging filter which represents a rectangular frequency response (sharp frequency cutoff). Let's simplify and just use a rectangular window (which has a sinc frequency response). It can be thought of as a simple moving average. As you slide through the data you make each pixel more...
How about you do a sliding transform on the data and see how the fft varies in time. I expect you will find that simply adjusting the phase does not really reverse you in time. It might be close for a very small increment in time, but all you are really doing is adjusting the phase...
The question becomes one of whether the orange will fly apart from the acceleration or air turbulence before it gets enough momentum to break the drywall.
http://www.gypsum.org/wp/wp-content/uploads/2011/11/GA-235-10.pdf [Broken] talks about drywall strength.
I'd have to learn more about the...
What do you mean by what do you mean by? (lol)
I think I know what you are asking, but I'm not sure how far I can take it. I'm just saying that the simplistic math assumes the slits and barriers are ideal. There is no reflection from internal surfaces of a thick barrier, that the boundaries...
The math for the double slit assumes infinitely thin perfect absorbers with perfect boundaries and interference free paths. To the extent that is not true, the results are distorted. The inherent vibration or uncertainty of the molecules at the boundaries and the resulting "non-ideal"...
I don't think the spinning matters. When you "throw" from a platform in space, whether by fling, by compressed air, or by a spring, momentum is conserved. m*v of projectiles and m*v of platform are equal and opposite. The same basic thing is true for the discuss thrower in spite of all the...
"Time is the forth dimension" is only referring to time as an arbitrary dimension in addition to the 3 spatial dimensions we are used to. There is nothing spatial about it in the sense of the 3 spatial dimensions we exist in.
Considering spatial dimensions you should think in terms of right...
The answer, as is often the case, is "it depends on the frequency response of the material".
If you think of a square wave in terms of it Fourier series, it is (roughly) the sum of infinite odd sine wave harmonics of decreasing amplitudes (1* (fundamental) + 1/3(third harmonic) + 1/5 (fifth...
Maybe this will help you, or intrigue you. A lecture by Richard Feynman on the nature of Light
http://www.vega.org.uk/video/subseries/8
lecture 1
http://www.vega.org.uk/video/programme/45
Great explanation of why glowing iron isn't "laser-pure". Saying they are not atomic transitions is pretty broad though since pure Iron in a rod exhibits atomic behavior (it's crystaline, not molecular, I think). I'm not familiar with the popular myth of "atomic transitions". They definitely...
If the mass changed but the force was constant you would re-write the equation to express the mass in time. You would then be able to solve for the acceleration as it changed in time. Or you could hold the acceleration constant and solve for the required force profile to match the mass change...
That's actually pretty easy. Reactance is modeled by (I hate this term) imaginary numbers, but in simple terms what happens is that there is a phase shift of 90 degrees between the voltage and current caused by the capacitor. The current through the capacitor leads the voltage (essentially it...
Since the capacitive reactance and the resistance are at right angles, you need to use the squareroot of the sum of the squares to determine the magnitude of the sum. What is the magnitude of Z = R + jw/C.
naturally? As in "unassisted in nature"? Don't think so. It can be done with 16 M-ev deuterons.
The wikipedia page on Plutonium describes the reaction in the Isotopes and synthesis section. Basically add a neutron which beta decays into a proton and voila, another element.
The Earth goes around the sun at 67,000 miles per hour. It will be moving towards you. You can guess how it clears it orbit (splat). If you are moving at the same velocity you will continue (to a first order) to orbit on opposite sides of the sun.
Gravity manifests itself as an attractive...
I meant to imply rigid or has inerta. It needs to present a discontinuity or boundary. I think your reflections are the key to approaching this. If there are no reflections from the sphere, it will not travel.
I didn't read through all your links so maybe I missed something. I have found...
I'll agree that to the extent that there is reflection there has to be energy transfer. But since the sphere is free to move up and down there will be little reflection. A weightless sphere would not cause a reflection and so would have no net motion. It seems that only to the extent that the...
I don't understand what transverse mechanism applies a net lateral force to the floating sphere. I'm talking a linear wave caused by a vertical displacement or vibration, not a breaking wave or net current.
Atmospheric pressure exerts a 14.7 pounds per square inch at sea level. Making 1 sq inch of glass withstand 14.7 pounds isn't very hard (Or 1/4 inch per side = less than 1 lb)
Say you have 2 shallow cylinders of 1 foot diameter = 113 square inches with a vacuum between them. That means it...
First let's just talk about 1 sphere bobbing and causing waves. What is its effect on a second sphere. I think there is no net water movement away from the first sphere. The second sphere will experience repetitive vertical and horizontal displacement in a repetitive pattern with no net long...
Yes, just like any other amplitude modulated signal.
No, just like any other amplitude modulated signal.
This of course assumes the system is completely linear. The waves cannot interact in a linear system other than interference pattern like effects.
Say you took a 9V battery and hooked it to switches so it could be reversed. Say you then connected it to a light bulb. As you flipped the switch over and back the current would flow one way and then the other. That would be square wave AC. If you could switch it over and back 60 times per...
since the acceleration of gravity is 9.8m/sec/sec, you can calculate the distance at which the vertical freefall distance in meters equals the velocity in meters/sec. It is meaningless though.
Say we have two 110VAC bulbs, each in a box with its own brightness meter and a switch and an adequate voltage source that can power both bulbs.
Turn on 1 bulb, its meter has a reading. Turn on the other bulb, its meter reads the same. The first meter does not change when you turn on the...
I always thought it was the gyro effect of the wheels, and that never intuitively seemed adequate. That description really hit the spot! leaning generates torque tending to steer you into the lean.