|MLA Citation:||Bloomfield, Louis A. "Other Topics" How Everything Works 22 Apr 2018. Page 7 of 11. 22 Apr 2018 <http://www.howeverythingworks.org/prints.php?topic=other&page=7>.|
But with computers and digital signal processing now commonplace, filtering has become much more sophisticated. Filters can now study an audio or video input signal over a long period of time and can even use data about future values of the input signal when producing an output signal. The filters that you ask about are all digital filters that produce an output signal that is related to the past, present, and future values of the input signal. A rectangular window filter is one that determines the output signal from a certain range of past, present, and future input signal values, all weighted evenly. A triangular or "Parzen" window filter is one that determines the output signal from a certain range of past, present, and future input signal values, with the weighting of values decreasing linearly with increasing time in the past or future. A Hanning window filter is one that determines the output signal from the complete past and future input signal values, with the weighting of values decreasing as the cosine of the time in the past or future (see for example, "Numerical Recipes" by Press, Flannery, Teukolsky, and Vetterling). All three filtering windows and filters are used to keep filters that extract certain frequency ranges from the input signal from affecting other frequency ranges. For that purpose, the Hanning window is better than the Parzen window and both are better than the rectangular window. As an example of the applications of these filters, a digital audio filter that makes good use of the Hanning window can enhance the treble of an audio signal uniformly without coloring the midrange at all. Earlier filters that only used past information always colored the midrange and didn't affect the treble uniformly.
To understand how their time passes more slowly that yours, you can think of the radio wave's frequency as the ticking of a clock. The time it takes the clock's ticks to reach your ear isn't important in measuring the passage of time. What you care about is how often those ticks occur. When you "listen" to the ticking of the clock on the big planet, it ticks 99 million times each second. However, to the people on the planet, it ticks 100 million times each second. This apparent inconsistency is explained by the fact that time is passing faster for you than for the people on the planet. Their second lasts longer than yours, which is why they count more ticks during their second than you count during your second.
The two classes of gravity wave detectors currently in development or operation are large cryogenic bar detectors and laser interferometric detectors. A cryogenic bar detector tries to observe gravity waves by looking for vibrational excitations of huge metal bars. When a strong gravity wave passes through one of these bars, it should excite various vibrations in the bar that can be detected by sensitive motion sensors. A laser interferometric detector tries to observe gravity waves by looking at distance changes in the arms of a laser interferometer—a huge mirror system with laser beams bouncing back and forth within it. When a strong gravity wave passes through the mirror system, it should change the spacings of the mirrors enough to cause variations in the optical characteristics of the interferometer (for more info, see www.ligo.caltech.edu). So far, no gravity waves have been observed definitively.
Take a very long string, say about 20 miles long, and attach one end of the string to a post. Now draw the string taut and walk all the way around the post while holding on to the other end of the string. If you measure the distance you walked while completing one full trip around the post, you would expect it to be related to the length of the string by a factor of 2 times pi because you learn in grade school that the circumference of a circle is 2 times pi times the radius of that circle. However, that relationship is only true if you're working on a flat surface. Since the earth is curved, the circumference of the circle around which you walk will be somewhat less than 2 times pi times the radius of the circle. That result is enough to prove that you're on a curved surface.
You can see this effect by performing the experiment I just suggested on the surface of a basketball. Take a short length of string and use it, together with a pin and a pencil, to draw a circle on the surface of the ball. If you measure the circumference of that circle and compare it to 2 times pi times the length of the string, the circle's circumference will be a bit shorter than expected. As with the earth, the basketball is a curved surface. The larger the circle you try to draw in this manner, the greater the discrepancy between 2 times pi times the radius and the actual circumference of the circle.
In a conductor, there are many unused levels available within easy reach of the electrons. If the electrons have to begin moving toward the left, in order to carry an electric current, some of the electrons that are in right-heading levels can shift into empty left-heading levels in order to let that current flow. But in an insulator, all of the easily accessible levels are filled and the electrons can't shift to other levels in order to carry current in a particular direction. While there are empty levels around, an electron would need a large increase in its energy to begin traveling in one of these empty levels. As a result, the electrons in an insulator can't carry an electric current.
One of the reasons that Hollywood ignores real physics so often is that real physics is almost wilder than fiction. Suppose that you decided to travel to a star 5 light-years away from the earth and that you have a starship that can almost reach the speed of light (another nearly impossible thing, but let's ignore that problem). If you travel to the star at almost the speed of light, make one loop around it, and head right back to earth, I will have aged 10 years while waiting for you to return. However, you will only have aged days or weeks, depending on just how close you came to the speed of light. During the trip, we will have disagreed on many physical quantities, particularly the times at which various events occurred and the distances between objects. The mixing of time and space that occur when two people move rapidly relative to one another would be so disorienting to movie or television viewers that Hollywood ignores or simplifies these effects.
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