The International System of Units (SI)
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Db Math Marco Zennaro Ermanno Pietrosemoli Goals
dB Math Marco Zennaro Ermanno Pietrosemoli Goals ‣ Electromagnetic waves carry power measured in milliwatts. ‣ Decibels (dB) use a relative logarithmic relationship to reduce multiplication to simple addition. ‣ You can simplify common radio calculations by using dBm instead of mW, and dB to represent variations of power. ‣ It is simpler to solve radio calculations in your head by using dB. 2 Power ‣ Any electromagnetic wave carries energy - we can feel that when we enjoy (or suffer from) the warmth of the sun. The amount of energy received in a certain amount of time is called power. ‣ The electric field is measured in V/m (volts per meter), the power contained within it is proportional to the square of the electric field: 2 P ~ E ‣ The unit of power is the watt (W). For wireless work, the milliwatt (mW) is usually a more convenient unit. 3 Gain and Loss ‣ If the amplitude of an electromagnetic wave increases, its power increases. This increase in power is called a gain. ‣ If the amplitude decreases, its power decreases. This decrease in power is called a loss. ‣ When designing communication links, you try to maximize the gains while minimizing any losses. 4 Intro to dB ‣ Decibels are a relative measurement unit unlike the absolute measurement of milliwatts. ‣ The decibel (dB) is 10 times the decimal logarithm of the ratio between two values of a variable. The calculation of decibels uses a logarithm to allow very large or very small relations to be represented with a conveniently small number. ‣ On the logarithmic scale, the reference cannot be zero because the log of zero does not exist! 5 Why do we use dB? ‣ Power does not fade in a linear manner, but inversely as the square of the distance. -
Appendix A: Symbols and Prefixes
Appendix A: Symbols and Prefixes (Appendix A last revised November 2020) This appendix of the Author's Kit provides recommendations on prefixes, unit symbols and abbreviations, and factors for conversion into units of the International System. Prefixes Recommended prefixes indicating decimal multiples or submultiples of units and their symbols are as follows: Multiple Prefix Abbreviation 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 10 deka da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y Avoid using compound prefixes, such as micromicro for pico and kilomega for giga. The abbreviation of a prefix is considered to be combined with the abbreviation/symbol to which it is directly attached, forming with it a new unit symbol, which can be raised to a positive or negative power and which can be combined with other unit abbreviations/symbols to form abbreviations/symbols for compound units. For example: 1 cm3 = (10-2 m)3 = 10-6 m3 1 μs-1 = (10-6 s)-1 = 106 s-1 1 mm2/s = (10-3 m)2/s = 10-6 m2/s Abbreviations and Symbols Whenever possible, avoid using abbreviations and symbols in paragraph text; however, when it is deemed necessary to use such, define all but the most common at first use. The following is a recommended list of abbreviations/symbols for some important units. -
Quantity Symbol Value One Astronomical Unit 1 AU 1.50 × 10
Quantity Symbol Value One Astronomical Unit 1 AU 1:50 × 1011 m Speed of Light c 3:0 × 108 m=s One parsec 1 pc 3.26 Light Years One year 1 y ' π × 107 s One Light Year 1 ly 9:5 × 1015 m 6 Radius of Earth RE 6:4 × 10 m Radius of Sun R 6:95 × 108 m Gravitational Constant G 6:67 × 10−11m3=(kg s3) Part I. 1. Describe qualitatively the funny way that the planets move in the sky relative to the stars. Give a qualitative explanation as to why they move this way. 2. Draw a set of pictures approximately to scale showing the sun, the earth, the moon, α-centauri, and the milky way and the spacing between these objects. Give an ap- proximate size for all the objects you draw (for example example next to the moon put Rmoon ∼ 1700 km) and the distances between the objects that you draw. Indicate many times is one picture magnified relative to another. Important: More important than the size of these objects is the relative distance between these objects. Thus for instance you may wish to show the sun and the earth on the same graph, with the circles for the sun and the earth having the correct ratios relative to to the spacing between the sun and the earth. 3. A common unit of distance in Astronomy is a parsec. 1 pc ' 3:1 × 1016m ' 3:3 ly (a) Explain how such a curious unit of measure came to be defined. Why is it called parsec? (b) What is the distance to the nearest stars and how was this distance measured? 4. -
Calculating Growing Degree Days by Jim Nugent District Horticulturist Michigan State University
Calculating Growing Degree Days By Jim Nugent District Horticulturist Michigan State University Are you calculating degree day accumulations and finding your values don't match the values being reported by MSU or your neighbor's electronic data collection unit? There is a logical reason! Three different methods are used to calculate degree days; i.e., 1) Averaging Method; 2) Baskerville-Emin (BE) Method; and 3) Electronic Real-time Data Collection. All methods attempt to calculate the heat accumulation above a minimum threshold temperature, often referred to the base temperature. Once both the daily maximum and minimum temperatures get above the minimum threshold temperature, (i.e., base temperature of 42degrees, 50degrees or whatever other base temperature of interest) then all methods are fairly comparable. However, differences do occur and these are accentuated in an exceptionally long period of cool spring temperatures, such as we experienced this year. Let me briefly explain: 1. Averaging Method: Easy to calculate Degree Days(DD) = Average daily temp. - Base Temp. = (max. + min.) / 2 - Base temp. If answer is negative, assume 0. Example: Calculate DD Base 50 given 65 degrees max. and 40 degrees min. Avg. = (65 + 40) / 2 = 52.5 degrees DD base 50 = 52.5 - 50 = 2.5 degrees. But look what happens given a maximum of 60 degrees and a minimum of 35 degrees: Avg. = (60 + 35) / 2 = 47.5 DD base 50 = 47.5 - 50 = -2.5 = 0 degrees. The maximum temperature was higher than the base of 50° , but no degree days were accumulated. A grower called about the first of June reporting only about 40% of the DD50 that we have recorded. -
New Realization of the Ohm and Farad Using the NBS Calculable Capacitor
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38, NO. 2, APRIL 1989 249 New Realization of the Ohm and Farad Using the NBS Calculable Capacitor JOHN Q. SHIELDS, RONALD F. DZIUBA, MEMBER, IEEE,AND HOWARD P. LAYER Abstrucl-Results of a new realization of the ohm and farad using part of the NBS effort. This paper describes our measure- the NBS calculable capacitor and associated apparatus are reported. ments and gives our latest results. The results show that both the NBS representation of the ohm and the NBS representation of the farad are changing with time, cNBSat the rate of -0.054 ppmlyear and FNssat the rate of 0.010 ppm/year. The 11. AC MEASUREMENTS realization of the ohm is of particular significance at this time because The measurement sequence used in the 1974 ohm and of its role in assigning an SI value to the quantized Hall resistance. The farad determinations [2] has been retained in the present estimated uncertainty of the ohm realization is 0.022 ppm (lo) while the estimated uncertainty of the farad realization is 0.014 ppm (la). NBS measurements. A 0.5-pF calculable cross-capacitor is used to measure a transportable 10-pF reference capac- itor which is carried to the laboratory containing the NBS I. INTRODUCTION bank of 10-pF fused silica reference capacitors. A 10: 1 HE NBS REPRESENTATION of the ohm is bridge is used in two stages to measure two 1000-pF ca- T based on the mean resistance of five Thomas-type pacitors which are in turn used as two arms of a special wire-wound resistors maintained in a 25°C oil bath at NBS frequency-dependent bridge for measuring two 100-kQ Gaithersburg, MD. -
8.1 Basic Terms & Conversions in the Metric System 1/1000 X Base Unit M
___________________________________ 8.1 Basic Terms & Conversions in the Metric System ___________________________________ Basic Units of Measurement: •Meter (m) used to measure length. A little longer than a yard. ___________________________________ ___________________________________ •Kilogram (kg) used to measure mass. A little more than 2 pounds. ___________________________________ •Liter (l) used to measure volume. A little more than a quart. •Celsius (°C) used to measure temperature. ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 1 The metric system is based on powers of 10 (the decimal system). ___________________________________ Prefix Symbol Meaning ___________________________________ kilo k 1000 x base unit ___________________________________ hecto h 100 x base unit deka da 10 x base unit ___________________________________ ——— ——— base unit deci d 1/10 x base unit ___________________________________ centi c 1/100 x base unit milli m 1/1000 x base unit ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 2 ___________________________________ Changing Units within the Metric System 1. To change from a smaller unit to a larger unit, move the ___________________________________ decimal point in the original quantity one place to the for each larger unit of measurement until you obtain the desired unit of measurement. ___________________________________ 2. To change form a larger unit to a smaller unit, move the decimal point -
What Time Is It?
The Astronomical League A Federation of Astronomical Societies Astro Note E3 – What Time Is It? Introduction – There are many methods used to keep time, each having its own special use and advantage. Until recently, when atomic clocks became available, time was reckoned by the Earth's motions: one rotation on its axis was a "day" and one revolution about the Sun was a "year." An hour was one twenty-fourth of a day, and so on. It was convenient to use the position of the Sun in the sky to measure the various intervals. Apparent Time This is the time kept by a sundial. It is a direct measure of the Sun's position in the sky relative to the position of the observer. Since it is dependent on the observer's location, it is also a local time. Being measured according to the true solar position, it is subject to all the irregularities of the Earth's motion. The reference time is 12:00 noon when the true Sun is on the observer's meridian. Mean Time Many of the irregularities in the Earth's motion are due to its elliptical orbit. In order to add some consistency to the measure of time, we use the concept of mean time. Mean time uses the position of a fictitious "mean Sun" which moves smoothly and uniformly across the sky and is insensitive to the irregularities of the Earth’s motion. A mean solar day is 24 hours long. The "Equation of Time," tabulated in almanacs and represented on maps by the analemma, provides the correction between mean and apparent time to allow for the eccentricity of the Earth's orbit. -
Units, Conversations, and Scaling Giving Numbers Meaning and Context Author: Meagan White; Sean S
Units, Conversations, and Scaling Giving numbers meaning and context Author: Meagan White; Sean S. Lindsay Version 1.3 created August 2019 Learning Goals In this lab, students will • Learn about the metric system • Learn about the units used in science and astronomy • Learn about the units used to measure angles • Learn the two sky coordinate systems used by astronomers • Learn how to perform unit conversions • Learn how to use a spreadsheet for repeated calculations • Measure lengths to collect data used in next week’s lab: Scienctific Measurement Materials • Calculator • Microsoft Excel • String as a crude length measurement tool Pre-lab Questions 1. What is the celestial analog of latitude and longitude? 2. What quantity do the following metric prefixes indicate: Giga-, Mega-, kilo-, centi-, milli-, µicro-, and nano? 3. How many degrees is a Right Ascension “hour”; How many degrees are in an arcmin? Arcsec? 4. Use the “train-track” method to convert 20 ft to inches. 1. Background In any science class, including astronomy, there are important skills and concepts that students will need to use and understand before engaging in experiments and other lab exercises. A broad list of fundamental skills developed in today’s exercise includes: • Scientific units used throughout the international science community, as well as units specific to astronomy. • Unit conversion methods to convert between units for calculations, communication, and conceptualization. • Angular measurements and their use in astronomy. How they are measured, and the angular measurements specific to astronomy. This is important for astronomers coordinate systems, i.e., equatorial coordinates on the celestial sphere. • Familiarity with spreadsheet programs, such as Microsoft Excel, Google Sheets, or OpenOffice. -
Lesson 1: Length English Vs
Lesson 1: Length English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter C. 1 inch or 1 centimeter English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 yard = 0.9444 meters English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 inch = 2.54 centimeters 1 yard = 0.9444 meters Metric Units The basic unit of length in the metric system in the meter and is represented by a lowercase m. Standard: The distance traveled by light in absolute vacuum in 1∕299,792,458 of a second. Metric Units 1 Kilometer (km) = 1000 meters 1 Meter = 100 Centimeters (cm) 1 Meter = 1000 Millimeters (mm) Which is larger? A. 1 meter or 105 centimeters C. 12 centimeters or 102 millimeters B. 4 kilometers or 4400 meters D. 1200 millimeters or 1 meter Measuring Length How many millimeters are in 1 centimeter? 1 centimeter = 10 millimeters What is the length of the line in centimeters? _______cm What is the length of the line in millimeters? _______mm What is the length of the line to the nearest centimeter? ________cm HINT: Round to the nearest centimeter – no decimals. -
The Avogadro Constant to Be Equal to Exactly 6.02214X×10 23 When It Is Expressed in the Unit Mol −1
[august, 2011] redefinition of the mole and the new system of units zoltan mester It is as easy to count atomies as to resolve the propositions of a lover.. As You Like It William Shakespeare 1564-1616 Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States and Venezuela 1875 -May 20 1875, BIPM, CGPM and the CIPM was established, and a three- dimensional mechanical unit system was setup with the base units metre, kilogram, and second. -1901 Giorgi showed that it is possible to combine the mechanical units of this metre–kilogram–second system with the practical electric units to form a single coherent four-dimensional system -In 1921 Consultative Committee for Electricity (CCE, now CCEM) -by the 7th CGPM in 1927. The CCE to proposed, in 1939, the adoption of a four-dimensional system based on the metre, kilogram, second, and ampere, the MKSA system, a proposal approved by the ClPM in 1946. -In 1954, the 10th CGPM, the introduction of the ampere, the kelvin and the candela as base units -in 1960, 11th CGPM gave the name International System of Units, with the abbreviation SI. -in 1970, the 14 th CGMP introduced mole as a unit of amount of substance to the SI 1960 Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Much improved atomic weight estimates, oxygen = 100 . Jöns Jacob Berzelius (1779–1848) Further improved atomic weight estimates . -
About SI Units
Units SI units: International system of units (French: “SI” means “Système Internationale”) The seven SI base units are: Mass: kg Defined by the prototype “standard kilogram” located in Paris. The standard kilogram is made of Pt metal. Length: m Originally defined by the prototype “standard meter” located in Paris. Then defined as 1,650,763.73 wavelengths of the orange-red radiation of Krypton86 under certain specified conditions. (Official definition: The distance traveled by light in vacuum during a time interval of 1 / 299 792 458 of a second) Time: s The second is defined as the duration of a certain number of oscillations of radiation coming from Cs atoms. (Official definition: The second is the duration of 9,192,631,770 periods of the radiation of the hyperfine- level transition of the ground state of the Cs133 atom) Current: A Defined as the current that causes a certain force between two parallel wires. (Official definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 Newton per meter of length. Temperature: K One percent of the temperature difference between boiling point and freezing point of water. (Official definition: The Kelvin, unit of thermodynamic temperature, is the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water. Amount of substance: mol The amount of a substance that contains Avogadro’s number NAvo = 6.0221 × 1023 of atoms or molecules. -
Decibels, Phons, and Sones
Decibels, Phons, and Sones The rate at which sound energy reaches a Table 1: deciBel Ratings of Several Sounds given cross-sectional area is known as the Sound Source Intensity deciBel sound intensity. There is an abnormally Weakest Sound Heard 1 x 10-12 W/m2 0.0 large range of intensities over which Rustling Leaves 1 x 10-11 W/m2 10.0 humans can hear. Given the large range, it Quiet Library 1 x 10-9 W/m2 30.0 is common to express the sound intensity Average Home 1 x 10-7 W/m2 50.0 using a logarithmic scale known as the Normal Conversation 1 x 10-6 W/m2 60.0 decibel scale. By measuring the intensity -4 2 level of a given sound with a meter, the Phone Dial Tone 1 x 10 W/m 80.0 -3 2 deciBel rating can be determined. Truck Traffic 1 x 10 W/m 90.0 Intensity values and decibel ratings for Chainsaw, 1 m away 1 x 10-1 W/m2 110.0 several sound sources listed in Table 1. The decibel scale and the intensity values it is based on is an objective measure of a sound. While intensities and deciBels (dB) are measurable, the loudness of a sound is subjective. Sound loudness varies from person to person. Furthermore, sounds with equal intensities but different frequencies are perceived by the same person to have unequal loudness. For instance, a 60 dB sound with a frequency of 1000 Hz sounds louder than a 60 dB sound with a frequency of 500 Hz.