Hi seercalf,

Welcome to the forum!

Hi math9maniac,

#4661. Find the area of a parallelogram whose length is 30 cm, width is 20 cm, and one diagonal is 40 cm.

Hi,

The solution #4659 is correct. Neat work, Monox D. I-Fly!

#4660. A boatman goes 2 kilometers against the current of the stream in 1 hour and goes 1 kilometer along the current in 10 minutes. How long will it take to go 5 kilometers in stationary water?

Hi,

#7542. Find the average of first nine prime numbers.

414) Differences in Microphones & Speakers

Although at first glance, microphones and speakers appear to be very different kinds of devices, they are in fact closely related. Speakers and microphones are both transducers -- components which transform energy from one type to another. A speaker turns electrical currents into sound waves; a microphone converts sound into electrical energy. The main differences between them lie in the way audio designers have optimized each to perform its particular task efficiently.

Speaker

A speaker produces sound when you drive it with an amplifier connected to an audio source. Most speakers use a electromagnet design in which a permanent magnet is situated in a metal frame that holds a cone made of paper or plastic. A wire coil attached to the end of the cone produces attractive and repulsive forces when electrical current flows through it; the pushing and pulling against the cone generates sound waves. The cone's size dictates the general frequency range it reproduces most efficiently: large cones produce low frequencies, and small ones generate high frequencies.

Microphone

When you speak or sing into a microphone, the sound waves of your voice produce vibrations in a diaphragm inside the mike. Although they have a variety of basic designs, a common type called the dynamic microphone uses a magnetic principle similar to that used in speakers. The diaphragm carries a lightweight wire coil made of fine wire; the coil moves through a magnetic field and produces electrical currents which mirror the incoming sound waves. Another popular design, called the condenser microphone, places the diaphragm on one of two metal plates separated by an insulator. The vibrations in the diaphragm produce changes in the electrical capacitance between the two plates. Condenser mics require a battery, as the capacitance effect doesn't produce electrical currents by itself.

Similarities

The dynamic microphone and standard speaker both employ a moving coil in a magnetic field, producing electrical currents from sound vibrations or vice-versa. It is possible, although risky, to connect a dynamic microphone to a speaker output and hear sound from the mic. As the microphone is not designed to handle electrical inputs, a loud amp setting can destroy the mic if used in this manner. In the same way, you can connect a speaker to a microphone input, but because a speaker doesn't make an ideal mike, you must yell into it to produce a detectable signal. Walkie-talkies and room intercom systems use a single speaker-microphone device that performs both functions moderately well.

Differences

Microphones produce a relatively weak output that requires preamplification to bring the signal to a standard line level. Because the signals are weak, microphone cables have shielding that reduces electrical noise picked up from fluorescent lights and appliances. A microphone picks up a wide range of frequencies with great sensitivity. The loudspeaker's purpose is to fill a room with high-fidelity sound. This means handling large amounts of power from an amplifier -- up to several hundred watts for some types of speakers. To manage the power, the speaker has a robust, heavy design. For good fidelity, a single speaker cabinet may have two or more separate speaker drivers, each suited to a particular frequency range; a single speaker does not have the wide range that a microphone has.

585) Hans Christian Gram

Hans Christian Joachim Gram (13 September 1853 – 14 November 1938) was a Danish bacteriologist noted for his development of the Gram stain, still a standard technique to classify bacteria and make them more visible under a microscope.

Early life and education

Gram was the son of Frederik Terkel Julius Gram, a professor of jurisprudence, and Louise Christiane Roulund.

He studied at the University of Copenhagen, and was an assistant in botany to the zoologist Japetus Steenstrup. His study of plants introduced him to the fundamentals of pharmacology and the use of the microscope.

Gram entered medical school in 1878 and graduated in 1883. He travelled throughout Europe between 1878 and 1885.

Career

Gram stain

In Berlin, in 1884, Gram developed a method for distinguishing between two major classes of bacteria. This technique, the Gram stain, continues to be a standard procedure in medical microbiology. This work gained Gram an international reputation. The stain later played a major role in classifying bacteria. Gram was a modest man, and in his initial publication he remarked, "I have therefore published the method, although I am aware that as yet it is very defective and imperfect; but it is hoped that also in the hands of other investigators it will turn out to be useful."

A Gram stain is made using a primary stain of crystal violet and a counterstain of safranin. Bacteria that turn purple when stained are called 'Gram-positive', while those that turn red when counterstained are called 'Gram-negative'.

Other work

Gram's initial work concerned the study of red blood cells in men. He was among the first to recognise that macrocytes were characteristic of pernicious anaemia.
In 1891, Gram taught pharmacology, and later that year was appointed professor at the University of Copenhagen. In 1900, he resigned his chair in pharmacology to become professor of medicine. As a professor, he published four volumes of clinical lectures which became widely used in Denmark. He retired from the University of Copenhagen in 1923, and died in 1938.

Popular recognition

On 13 September 2019, Google commemorated the anniversary of his birth with a Doodle for Canada, Peru, Argentina, Australia, New Zealand, Israel, India and some European countries.

Hi,

#7355. What is 'Pulitzer Prize' awarded for?

#7356. What is 'Hyatt Hotels Corporation' known for?

413) Telescope

The telescope is an instrument that collects and analyzes the radiation emitted by distant sources. The most common type is the optical telescope, a collection of lenses and/or mirrors that is used to allow the viewer to see distant objects more clearly by magnifying them or to increase the effective brightness of a faint object. In a broader sense, telescopes can operate at most frequencies of the electromagnetic spectrum, from radio waves to gamma rays. The one characteristic all telescopes have in common is the ability to make distant objects appear to be closer. The word telescope is derived from the Greek tele meaning far, and skopein meaning to view.
The first optical telescope was probably constructed by German-born Dutch lensmaker Hans Lippershey (1570–1619), in 1608. The following year, Italian astronomer and physicist Galileo Galilei (1564– 1642) built the first astronomical telescope, from a tube containing two lenses of different focal lengths aligned on a single axis (the elements of this telescope are still on display in Florence, Italy). With this telescope and several following versions, Galileo made the first telescopic observations of the sky and discovered lunar mountains, four of Jupiter’s moons, sunspots, and the starry nature of the Milky Way galaxy. Since then, telescopes have increased in size and improved in image quality. Computers are now used to aid in the design of large, complex telescope systems.

Operation Of A Telescope

Light gathering

The primary function of a telescope is that of radiation gathering, in many cases light gathering. As will be seen below, resolution limits on telescopes would not call for an aperture much larger than about 30 in (76 cm). However, there are many telescopes around the world with diameters several times this value. The reason for this occurrence is that larger telescopes can see further because they can collect more light. The 200 in (508 cm) diameter reflecting telescope at Mt. Palomar, California, for instance can gather 25 times more light than the 40 in (102 cm) Yerkes telescope at Williams Bay, Wisconsin, the largest refracting telescope in the world. The light gathering power grows as the area of the objective increases, or the square of its diameter if it is circular. The more light a telescope can gather, the more distant the objects it can detect, and therefore larger telescopes increase the size of the observable universe.

Resolution

The resolution, or resolving power, of a telescope is defined as being the minimum angular separation between two different objects that can be detected.

Unfortunately, astronomers are not able to increase the resolution of a telescope simply by increasing the size of the light gathering aperture to as large a size as is need. Disturbances and non-uniformities in the atmosphere limit the resolution of telescopes positioned on the surface of Earth to somewhere in the range 0.5 to 2 arc seconds, depending on the location of the telescope. Telescope sights on top of mountains are popular since the light reaching the instrument has to travel through less air, and consequently the image has a higher resolution. However, a limit of 0.5 arc seconds corresponds to an aperture of only 12 in (30 cm) for visible light: larger telescopes do not provide increased resolution but only gather more light.

Magnification

Magnification is not the most important characteristic of telescopes as is commonly thought. The magnifying power of a telescope is dependent on the type and quality of eyepiece being used. The magnification is given simply by the ratio of the focal lengths of the objective and eyepiece. Thus, a 0.8 in (2 cm) focal length eyepiece used in conjunction with a 39 in (100 cm) focal length objective will give a magnification of 50. If the field of view of the eyepiece is 20°, the true field of view will be 0.4°.

Types Of Telescope

Most large telescopes built before the twentieth century were refracting telescopes because techniques were readily available to polish lenses. Not until the latter part of the nineteenth century were techniques developed to coat large mirrors, which allowed the construction of large reflecting telescopes.

Refracting telescopes

The parallel light from a distant object enters the objective, of focal length f1, from the left. The light then comes to a focus at a distance f1 from the objective. The eyepiece, with focal length f2, is situated a distance f1+ f2 from the objective such that the light exiting the eyepiece is parallel. Light coming from a second object (dashed lines) exits the eyepiece at an angle equal to f1/f2 times the angle of the light entering.

Refracting telescopes, i.e., telescopes that use lenses, can suffer from problems of chromatic and other aberrations, which reduce the quality of the image. In order to correct for these, multiple lenses are required, much like the multiple lens systems in a camera lens unit. The advantages of the refracting telescope include having no central stop or other diffracting element in the path of light as it enters the telescope, and the stability of the alignment and transmission characteristics over long periods of time. However, the refracting telescope can have low overall transmission due to reflection at the surface of all the optical elements. In addition, the largest refractor ever built has a diameter of only 40 in (102 cm): lenses of a larger diameter will tend to distort under their own weight and give a poor image. Additionally, each lens needs to have both sides polished perfectly and be made from material that is of highly uniform optical quality throughout its entire volume.

Reflecting telescopes

All large telescopes, both existing and planned, are of the reflecting variety. Reflecting telescopes have several advantages over refracting designs. First, the reflecting material (usually aluminum), deposited on a polished surface, has no chromatic aberration. Second, the whole system can be kept relatively short by folding the light path, as shown in the Newtonian and Cassegrain designs below. Third, the objectives can be made very large, since there is only one optical surface to be polished to high tolerance, the optical quality of the mirror substrate is unimportant and the mirror can be supported from the back to prevent bending. The disadvantages of reflecting systems are 1) alignment is more critical than in refracting systems, resulting in the use of complex adjustments for aligning the mirrors and the use of temperature insensitive mirror substrates and 2) the secondary or other auxiliary mirrors are mounted on a support structure that occludes part of the primary mirror and causes diffraction.

These are a) the prime focus, where the detector is simply placed at the prime focus of the mirror; b) the Newtonian, where a small, flat mirror reflects the light out to the side of the telescope; c) the Cassegrain, where the focus is located behind the plane of the primary mirror through a hole in its center and d) the Coudè, where the two flat mirrors provide a long focal length path as shown.

Catadioptric telescopes

Catadioptric telescopes use a combination of lenses and mirrors in order to obtain some of the advantages of both. The best-known type of catadioptric is the Schmidt telescope or camera, which is usually used to image a wide field of view for large area searches. The lens in this system is very weak and is commonly referred to as a corrector-plate.

Overcoming Resolution Limitations

The limits to the resolution of a telescope are, as described above, a result of the passage of the light from the distant body through the atmosphere, which is optically non-uniform. Stars appear to twinkle because of constantly fluctuating optical paths through the atmosphere, which results in a variation in both brightness and apparent position. Consequently, much information is lost to astronomers simply because they do not have sufficient resolution from their measurements. There are three ways of overcoming this limitation, namely setting the telescope out in space in order to avoid the atmosphere altogether, compensating for the distortion on a ground-based telescope, and/or stellar interferometry. The first two methods are innovations of the 1990s and have lead to a new era in observational astronomy.

Space Telescopes

The best known and biggest orbiting optical telescope is the Hubble Space Telescope (HST), which has an 8 ft (2.4 m) primary mirror and five major instruments for examining various characteristics of distant bodies. After a much-publicized problem with the focusing of the telescope and the installation of a package of corrective optics in 1993, the HST has proved to be the finest of all telescopes ever produced. The data collected from HST is of such a high quality that researchers can solve problems that have been in question for years, often with a single photograph. The resolution of the HST is 0.02 arc seconds, close to the theoretical limit since there is no atmospheric distortion, and a factor of around twenty times better than was previously possible. An example of the significant improvement in imaging that space-based systems have given is the Doradus 30 nebula, which prior to the HST was thought to have consisted of a small number of very bright stars. In a photograph taken by the HST it now appears that the central region has over 3,000 stars.

Another advantage of using a telescope in orbit about Earth is that the telescope can detect wavelengths such as the ultraviolet and various portions of the infrared, which are absorbed by the atmosphere and not detectable by ground-based telescopes.

Adaptive Optics

In 1991, the United States government declassified adaptive optics systems (systems that remove atmospheric effects), which had been developed under the Strategic Defense Initiative for ensuring that a laser beam could penetrate the atmosphere without significant distortion.

A laser beam is transmitted from the telescope into a layer of mesospheric sodium at 56–62 mi (90– 100 km) altitude. The laser beam is resonantly backscattered from the volume of excited sodium atoms and acts as a guide-star whose position and shape are well defined except for the atmospheric distortion. The telescope collects the light from the guide-star and a wavefront sensor determines the distortion caused by the atmosphere. This information is then fed back to a deformable mirror, or an array of many small mirrors, which compensates for the distortion. As a result, stars that are located close to the guide-star come into a focus, which is many times better than can be achieved without compensation. Telescopes have operated at the theoretical resolution limit for infrared wavelengths and have shown an improvement in the visible region of more than ten times. Atmospheric distortions are constantly changing, so the deformable mirror has to be updated every five milliseconds, which is easily achieved with modern computer technology.

Recording Telescope Data

Telescopes collect light largely for two types of analysis, imaging and spectrometry. The better known is imaging, the goal of which is simply to produce an accurate picture of the objects that are being examined. In past years, the only means of recording an image was to take a photograph. For long exposure times, the telescope had to track the sky by rotating at the same speed as the Earth, but in the opposite direction. This is still the case today, but the modern telescope no longer uses photographic film but a charge-coupled device (CCD) array. The CCD is a semiconductor light detector, which is fifty times more sensitive than photographic film, and is able to detect single photons. Being fabricated using semiconductor techniques, the CCD can be made to be very small, and an array typically has a spacing of 15 microns between CCD pixels. A typical array for imaging in telescopes will have a few million pixels. There are many advantages of using the CCD over photographic film or plates, including the lack of a developing stage and the output from the CCD can be read directly into a computer and the data analyzed and manipulated with relative ease.

The second type of analysis is spectrometry, which means that the researcher wants to know what wavelengths of light are being emitted by a particular object. The reason behind this is that different atoms and molecules emit different wavelengths of light—measuring the spectrum of light emitted by an object can yield information as to its constituents. When performing spectrometry, the output of the telescope is directed to a spectrometer, which is usually an instrument containing a diffraction grating for separating the wavelengths of light. The diffracted light at the output is commonly detected by a CCD array and the data read into a computer.

Modern Optical Telescopes

For almost 40 years the Hale telescope at Mt. Palomar (San Diego, California) was the world’s largest with a primary mirror diameter of 200 in (5.1 m). During that time, improvements were made primarily in detection techniques, which reached fundamental limits of sensitivity in the late 1980s. In order to observe fainter objects, it became imperative to build larger telescopes, and so a new generation of telescopes is being developed for the 2000s and beyond. These telescopes use revolutionary designs in order to increase the collecting area; 2,260 square feet (210 square meters) is being used for the European Southern Observatory (ESO), which operates observatories in Chile; the organization is headquartered near Munich, Germany.

This new generation of telescopes does not use the solid, heavy primary mirror of previous designs, whose thickness was between one-sixth and one-eighth of the mirror diameter. Instead, it uses a variety of approaches to reduce the mirror weight and improve its thermal and mechanical stability, including using many hexagonal mirror elements forming a coherent array; a single large meniscus mirror (with a thickness one-fortieth of the diameter), with many active support points which bend the mirror into the correct shape; and, a single large mirror formed from a honeycomb sandwich. In 2005, one of the first pictures taken by ESO was of 2M1207b, an exo-solar planet (a planet orbiting a star other than the sun) orbiting a brown dwarf star about 260 light-years away (where one light-year is the distance that light travels in vacuum in one year). These new telescopes, combined with quantum-limited detectors, distortion reduction techniques, and coherent array operation allow astronomers to see objects more distant than have been observed before.

One of this new generation, the Keck telescope located on Mauna Kea in Hawaii, is currently the largest operating optical/infrared telescope, using a 32 ft (10 m) effective diameter hyperbolic primary mirror constructed from 36 6-ft (1.8-m) hexagonal mirrors. The mirrors are held to relative positions of less than 50 nm using active sensors and actuators in order to maintain a clear image at the detector.

Because of its location at over 14,000 ft (4,270 m), the Keck is useful for collecting light over the range of 300 nm to 30 æm. In the late 1990s, Keck I was joined by an identical twin, Keck II. Then, in 2001, the two telescopes were linked together through the use of interferometry for an effective mirror diameter of 279 ft (85 m).

Alternative Wavelengths

Most of the discussion so far has been concerned with optical telescopes operating in the range from 300 to 1,100 nanometers (nm). However, valuable information is contained in the radiation reaching Earth at different wavelengths and telescopes have been built to cover wide ranges of operation, including radio and millimeter waves, infrared, ultraviolet, x rays, and gamma rays.

Infrared telescopes

Infrared telescopes are particularly useful for examining the emissions from gas clouds. Since water vapor in the atmosphere can absorb some of this radiation, it is especially important to locate infrared telescopes in high altitudes or in space. In 1983, NASA launched the highly successful Infrared Astronomical Satellite, which performed an all-sky survey, revealing a wide variety of sources and opening up new avenues of astrophysical discovery. With the improvement in infrared detection technology in the 1980s, the 1990s saw several new infrared telescopes, including the Infrared Optimized Telescope, a 26 ft (8 m) diameter facility, on Mauna Kea, Hawaii. In August 2003, NASA launched the Spitzer Space Telescope (formerly the Space Infrared Telescope Facility; named after Lyman Spitzer, Jr., who first suggested placing telescopes in orbit in the 1940s). It is in orbit about the sun (a heliocentric orbit), in which it follows behind Earth’s orbit about the sun, slowly receding away from Earth each year. Its primary mirror is about 2.8 ft (85 cm) in diameter, with a focal length that is twelve times the diameter of the primary mirror.
Several methods are used to reduce the large thermal background that makes viewing infrared difficult, including the use of cooled detectors and dithering the secondary mirror. This latter technique involves pointing the secondary mirror alternatively at the object in question and then at a patch of empty sky. Subtracting the second signal from the first results in the removal of most of the background thermal (infrared) noise received from the sky and the telescope itself, thus allowing the construction of a clear signal.

Radio telescopes

Radio astronomy was developed following World War II, using the recently developed radio technology to look at radio emissions from the sky. The first radio telescopes were very simple, using an array of wires as the antenna. In the 1950s, the now familiar collecting dish was introduced and has been widely used ever since.
Radio waves are not susceptible to atmospheric disturbances like optical waves are, and so the development of radio telescopes over the past forty years has seen a continued improvement in both the detection of faint sources as well as in resolution. Despite the fact that radio waves can have wavelengths which are meters long, the resolution achieved has been to the sub-arc second level through the use of many radio telescopes working together in an interferometer array, the largest of which stretches from Hawaii to the United States Virgin Islands (known as the Very Long Baseline Array). The largest working radio telescope is the Giant Meterwave Radio Telescope in India. It contains 14 telescopes arranged around a central square and another 16 positioned within three arms of a Y-shaped array. Its total interferometric baseline is about 15.5 mi (25 km). Construction is being made on the Low Frequency Array (LOFAR), which is a series of radio telescopes located across the Netherlands and Germany. As of September 2006, LOFAR has been constructed and is in the testing stage. When operational, it will have a total collecting area of around 0.4

KEY TERMS

Chromatic aberration —The reduction in image quality arising from the fact that the refractive index in varies across the spectrum.
Objective —The large light collecting lens used in a refracting telescope.
Reflecting telescope —A telescope that uses only reflecting elements, i.e., mirrors.
Refracting telescope —A telescope that uses only refracting elements; i.e., lenses.
Spectrometry —The measurement of the relative strengths of different wavelength components that make up a light signal.

584) Gordon Gould

Gordon Gould, in full Richard Gordon Gould, (born July 17, 1920, New York, N.Y., U.S.—died Sept. 16, 2005, New York), American physicist who played an important role in early laser research and coined the word laser (light amplification by stimulated emission of radiation).

Gould received a bachelor’s degree in physics from Union College in Schenectady, N.Y., in 1941 and a master’s degree in physics from Yale University two years later. He then worked on the Manhattan Project but was released from the project because of his membership in a communist political group (which he left in 1948). He started teaching physics at the City College of New York in 1946, and he entered graduate school at Columbia University, New York City, in 1949.

He came up with the idea of the laser and its name in 1957. He had discussed the idea with physicist Charles Townes, who had invented the maser, which amplified microwave radiation. Gould took Townes’s advice that he should write down his ideas and notarize them as a first step of applying for a patent. Gould left Columbia and joined the defense research firm Technical Research Group (TRG) in 1958 to work on building a laser. Believing that he first needed to have a working prototype, he waited until 1959 to apply for a patent, but by that time Townes and physicist Arthur Schawlow had filed such an application and his was rejected. With the initial support of TRG and with his notarized notebook as his main piece of evidence, Gould fought Townes and Schawlow’s award of the laser patent. After many years of litigation, he prevailed, and in 1977 he was issued the first of the four U.S. basic laser patents that he was eventually granted. The laser industry then fought the award of patents to Gould to avoid paying him millions of dollars in royalties, but he finally prevailed in 1987.

During the legal struggle over the laser patents, Gould taught at the Polytechnic Institute of New York from 1967 to 1973, and he founded an optical communications company, Optelecom, in 1973. He retired from Optelecom in 1985, and he was inducted into the (U.S.) National Inventors Hall of Fame in 1991.

Hi,

#7541. What is the least number to be added to 4523 to make it a perfect square?