How does Function Generator produce Sine Wave?

While there are different kind of function generators which have different modes of generating waveforms, I will tell you how a typical function generator produces sine wave. It all begins with generating a triangle waveform. Yes, all kinds of waveforms can be generated by a triangle wave. This is called as Oscillator source waveform. This is created by continuous charging and discharging of a capacitor. A comparator is used to constrain the output in specific upper and lower bounds. The circuitry (usually current and capacitor size) controls the frequency and amplitude of this source wave.This triangular ramp can now be modified into any of the waveforms by introducing logical circuits into the former. The user can control the output function through the physical interface of the device and particular part of circuit gets activated to create the desired output. The triangular signal is fed into waveform shaping circuit which includes additional diodes/transistors which chip off the peaks and add needed rounded-ness to form a sine waveform estimation.

Astronomy: Why do Mars and the other planets seem as stars in the sky, having different colors, such as red?

Even the nearest star after Sun appears as a point disc with an ordinary telescope. So, light from far stars go through thick atmosphere of the Earth (refraction!) and appears as what we call as twinkling. However, light coming from a planet does not seem to twinkle. The thumb rule is that the closer the celestial body to us, the lesser it will appear to scintillate. It happens because they appear bigger than stars and light from edges of the planet cancel this kind of random refraction through the atmosphere.

Due to increasing city lights and pollution, the planets are appearing fainter and fainter. The pollution layer is juxtaposed over the space view and reduces the actual color information. This is like putting a translucent rice paper above a red apple. You will see it lesser red. That is why it is really difficult to point out the color of the celestial body. I believe you can see Mars and other planets in near true color when seen from places away from city lights and pollution.

An interesting fact worth mentioning about Mars is that, it sometimes goes further from Sun than Earth from Sun. This causes it to appear brighter or dimmer (based on proximity to Sun). When dimmer and low in the horizon, it might also appear to scintillate.

How did scientists come to know that there exist millions of galaxies in the universe?

This is tough to calculate. Fortunately, we have a method to estimate this value. To do this, scientists can observe a region in the sky and count the number of galaxies (with the help of computers) in that region. This observed region is called as sample region. Scientists can then estimate the number of galaxies in the whole sky by multiplying the number of galaxies in the first case, with the number equivalent of how many such sample regions would fit in the entire sky. This method is called as Extrapolation. It is the process of estimating, beyond the original observation range, the value of a variable by its relationship with another variable.

Now, you would say that this value might be incorrect because all regions may not contain an equal number of galaxies. Yes, that might be true. Extrapolation allows us only to estimate. The preciseness of the value relies on the size of sampling region. And yes, the value is only valid for observable universe.

While estimates among different experts vary, an acceptable range is between 100 billion and 200 billion galaxies, Mario Livio, an astrophysicist at the Space Telescope Science Institute in Baltimore.

Also, you might be interested in reading this: NASA – Hubble Goes to the eXtreme to Assemble Farthest-Ever View of the Universe. The same method can also apply to find out the number of trees on the Earth or even finding the total number of runs that a team would make during a cricket match.

What is the frequency of Cosmic Rays?

Their name might deceive you but they actually do not share a part in the electromagnetic spectrum.

“The term ray is a historical accident, as cosmic rays were at first, and wrongly, thought to be mostly electromagnetic radiation. In common scientific usage, high-energy particles with intrinsic mass are known as “cosmic” rays, and photons, which are quanta of electromagnetic radiation (and so have no intrinsic mass) are known by their common names, such as “gamma rays” or “X-rays”, depending on their origin.”

They are high energy charged particles and travel at about the speed of light. They may contain particles with multiple energies and hence it is difficult to point out specific frequency for the cosmic rays. The frequency decreases with increasing energy of the particles.

“If you were to plot “cosmic rays” on an electromagnetic spectrum, it would basically encompass x-rays and everything higher in energy (higher in frequency or shorter in wavelength). I personally would leave it out, since I don’t think it’s a correct usage of “cosmic rays” (but I don’t make the rules).”
Dr. Eric Christian, NASA

So, the frequency at which cosmic rays must be operating would be anywhere more than 30EHz.