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936. What is the definitions of a "Hanning window", a "rectangular window", and a "triangular window"? — CV, Cape Town, South Africa
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In the days before digital signal processing, the filters that were available for audio or video systems were very simple. These filters monitored the audio or video signal and produced an output signal that was related to the present input signal and to that signals value's in the recent past. Such simple filters could enhance or diminish certain ranges of frequencies and were able to perform basic tasks such as adjusting the balance between treble, midrange, and bass in an audio system.

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.


943. Why do neutrinos only spin left? — BA, Fairbury, IL
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The absence of right-handed neutrinos is simply a feature of our universe and I don't believe anyone has a good explanation for their absence. Actually, it's still possible that right-handed neutrinos exist, but if they do exist, then they don't interact with other matter by way of any known force other than gravity. Even left-handed neutrinos barely interact with matter—they experience only gravity and the weak force, and usually pass through the entire earth without being absorbed. It could be that right-handed neutrinos are also present but that they don't even experience the weak force.

960. How does gravity influence the passage of time? — AW, Karachi, Pakistan
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Gravity's effects on time are the result of general relativity. Any concentration of mass/energy curves the space/time around it, which is ultimately why objects passing near that mass/energy are deflected. This curvature of space/time also slows the passage of time for objects that are near the concentration of mass/energy. To see why this slowing of time must occur, imagine people operating a radio transmitter on the surface of a very massive planet. They transmit their radio wave at exactly 100 MHz. You are far from the planet with your radio receiver and you begin trying to find their transmission. You will find it at a lower frequency, perhaps 99 MHz. That's because their radio wave has had to struggle to escape from the planet's gravity and has used up some of its energy in the process. Since energy is proportional to frequency, the radio wave shifts toward lower frequency as it climbs out of the planet's gravitational well to reach your receiver. Since the people on the planet think that their system is operating at 100 million oscillations per second and you think that it is operating at only 99 million oscillations per second, the people on the planet are evidently experiencing time more slowly than you are. Their second actually lasts longer than yours.

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.


961. How does water divining work? — GD, Mansfield, Australia
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I'm afraid that I remain unconvinced that water divining works at all. I believe that the whole issue is psychological—the power of suggestion. A divining rod will twist when something exerts a torque on it but there is no special force between the rod and water that would exert an unusual torque on the rod.

989. What exactly are gravity waves and how are they measured? — AY, Wayne, PA
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Gravity waves are deformations of space/time that propagate through space at the speed of light. While many motions of matter and energy are thought to emit gravity waves, those waves are normally extraordinarily weak. The only sources of detectable gravity waves are probably collapsing and colliding stars. Careful studies of the dynamics of binary star systems have shown that they also emit reasonably strong gravity waves, but those waves haven't been detected directly.

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.


1006. How does one prove that the earth is round?
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There are many possibilities, so I'll suggest an intriguing method that is familiar to surveyors. While the overly simple technique I suggest isn't particularly practical, it is closely related to surveying techniques that are practical.

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.


1033. How do conductors and insulators work? — SN, Beverly, MA
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Because of the quantum physic that dominates the behaviors of tiny objects in our universe, electrons can't travel in every path you can imagine; they can only travel in one of the paths that are allowed by quantum physics—paths that are called orbitals in atoms and levels in solids. When a material is assembled out of its constituent atoms, those atoms bring with them both their electrons and their quantum orbitals. These orbitals merge and blend as the atoms touch and they shift to form bands of levels in the resulting solid. The electrons in this solid end up traveling in the levels with the lowest energies. Because of the Pauli exclusion principle, only one indistinguishable electron can travel in each level. Since there are effectively two types of electrons, spin-up and spin-down, only two electrons can travel in each level of the solid.

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.


1034. How far away is the moon?
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It's about 235,000 miles (375,000 kilometers) away from the earth's surface. However, it's drifting about 1.3 inches (3.5 centimeters) farther away every year. That's because tides on the rotating earth gently pull the moon forward in its orbit as they slowly extract energy from the earth's rotation. Because of this transfer of energy from the earth's rotation to the moon's orbit, the moon is gradually slipping farther away from the earth.

1035. How fast does the earth wobble and why does it wobble? — MF, Tokyo, Japan
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The earth's rotational axis wobbles around in a circle once every 25,800 years because of torques (twists) exerted on it by the moon's gravity. The moon's gravity is able to twist the earth slightly because the earth isn't quite spherical. The earth's rotation causes it to bulge outward a little around its equator and it is this bulging that allows the moon to exert a torque on the earth.

1036. My husband and I watch Star Trek often. He says that travel at warp speeds (faster than the speed of light) is impossible and that Einstein's theories prove it. Is this true? — JL, Las Cruces, NM
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I'm afraid that travel at or above light speed is simply impossible and that "warp speed" travel is just a Hollywood fantasy. Einstein's special relativity forbids objects with mass from reaching or exceeding the speed of light and even if there were some way to travel vast distances in less time than it would take light to cover those distances, but without actually traveling at light speed, such travel would violate some important principles of causality—you would be able to meet your own grandparents as children and that sort of thing.

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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