Transcript: What is the meaning of a sine wave? The sine wave (also known as sinusoid) is a smooth oscillation. It is the graph of the sine function. It also proves the sine function, Sin(/) = opp/hype. Sine wave -Jack Clayton and osama Amplitude http://www.purplemath.com/modules/triggrph.htm The amplitude of a sine wave is the maximum distance it ever reaches from zero. Since the sine function varies from +1 to -1, the amplitude is one. In general, a sine wave is given by the formula: A= Sin(wt) where A is amplitude. In electrical voltage measurements, amplitude is sometimes used to mean the peak-to-peak voltage (Vpp) . This number will be twice the mathematical amplitude. The frequency of a sine wave is the number of complete cycles that happen every second. (A cycle is the same as the period, see below.) In the bouncing weight above, the frequency is about one cycle per second. Frequency used to be measured in cycles per second, but now we use the unit of frequency - the Hertz (abbreviated Hz). One Hertz (1Hz) is equal to one cycle per second. So the weight above is bouncing with a frequency of about 1Hz. The sound wave corresponding to Middle C on a piano is around 256Hz. If you tune your FM radio to 90.3, the radio wave carrying it has a frequency of 90.3MHz - or 90.3 megaHertz - 90.3 million cycles per second. Frequency
Transcript: Why the 21st? Electrical Current Roller Coaster Everything was the pretty much the same, meaning the B and D values are the same except C. The value of C is different because it symbolizes the difference month that is to spring from January. In addition the Value A is different because it symbolize the distance of the city to the equator. Real life would be like a roller coaster. C is the inital start and A is the distance from the inital start. Satellite y=a sin (bx+c) + d A - the smaller amplitude the less light varies from average, which is 12. In other words, the bigger the amp. and farther away from equator the more changes of daylight y=a sin (bx+c) + d Chicago The earth is further away from the sun in summer than winter. This concept relates to the value A, which w as the farther away from the equator the more daylight. In addition the dates of maximum tilt of the Earth's equator correspond to the Summer Solstice and Winter solstice. Five applications D - average amount of daylight in the city The number of hours of daylight for a given latitude, over the course of a year, is like a sinusoidal, with the peak at the summer solstice, and the trough at the winter solstice. C is the number of months that is move to spring from January - C goes up meaning the graph goes up ex. - C is north and is the month of October (-3) - + C goes up meaning the graph goes down ex. +C is south and is the month of March(+3) Must factor B value y=a sin (bx+c) + d y=3xSin(0.51x + 1.49) + 12.09 Daylight Sine Wave Ocean Tides Shanghai: Y = 2 x sin 0.51 x 1 - 1.51) + 12.13 y=a sin (bx+c) + d B - very similiar to 0.51 period = 2pie/B 2pie/B = 12.3 12 stands for months in year 3 is leap year Ferris wheel Summer/Winter Soltice Similiarities/ Differences Melbourne Y = 3xsin(0.51 x + 1.66) + 12.19
Transcript: Sine Waves - Microwaves Angela Cho 22/06/2020 What is Microwave? Microwave is a part of the electromagnetic spectrum that contains infrared waves, radio waves, ultraviolet radiation, and etc... between infrared and radio waves not visible Microwave Application of Microwave Microwave oven Wireless network Cancer treatement Radio astronomy Remote sensing etc... Application Wave Since Microwave is one part of Electromagnetic spectrum, which contains 7 types of wave, it is definitely an example of wave. Wave Graph Microwave graph This is the graph of microwave field by recording the fluorescence as a function of the time when a resonant 15 µs microwave pulse is applied. What is Sine Wave / Sinusoidal Wave? Definition It is a mathematical curve that describes a periodic oscillation. It is a continuous wave. It goes from 0 to 360 degrees. Sine Regression What is Sine Regression? Sine regression is derived from the sinusoidal regression, which is a relationship between dependent and independent variables of periodic oscillation , in a way that is written in the from of sine wave. Equation for Sine Regression Equation y = Asin(B(x - C)) + D where, IAI = amplitude B = frequency period = 2π/B C = horizontal shift (C>0 means right, C<0 means left) D = vertical shift (D>0 means up, D<0 means down) Sine Regression used with Microwave Application Sine Regression is used for the Remote sensing, which is one of the applicatin of Microwave. How is Sine Regression used for Remote sensing? How? Sine Regression curve is used for the Remote sensing in order to estimate the irradiance at the time of acquisition of radiance observations of the targets, so as to calculate target reflectance. Thank you ! Merci
Transcript: For "opposite" and the "adjacent" side (tangent), etc. To define the trigonometric functions for an acute angle A, start with any right triangle that contains the angle A. The three sides of the triangle are named as follows: The adjacent side is the side that is in contact with (adjacent to) both the angle we are interested in (angle A) and the right angle, in this case side b. The hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle. The opposite side is the side opposite to the angle we are interested in (angle A), in this case side a. In trigonometry, a unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the positive half of the x-axis, intersect the unit circle. The x- and y-coordinates of this point of intersection are equal to cos θ and sin θ, respectively. The point's distance from the origin is always 1. Unlike the definitions with the right or left triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can also be achieved by requiring certain symmetries and that sine be a periodic function. History Small help to remember trigonometric functions Sine Wave By Michal Pocinek Geometry Tangent where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), and D is the diameter of the triangle's circumcircle. When the last part of the equation is not used, sometimes the law is stated using the reciprocal: Sine Law Sine wave for my project SOH: Sinus, opposite hypotenuse The following are examples of how to solve a problem using the law of sines: Given: side a = 20, side c = 24, and angle C = 40° Using the law of sines, we conclude that While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. However calculating this may result in numerical error if an angle is close to 90 degrees. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an ambiguous case. The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, with the other being the law of cosines. -Sine wave can be imagined as a sea wave -It have infinity of possible ways to draw it. -Working with sine wave we use : The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law, Cosinus Right angle triangle CAH Cosinus, adjacent / hypotenuse Sinus is not the only function used to calculate the sides in a triangle. It can not be used every time so there are other two functions. All of these three functions can be used only in the right angle triangle. In mathematics, the sine function is a trigonometric function of an angle. The sine of an angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to (divided by) the length of the longest side of the triangle (i.e. the hypotenuse). SOH CAH TOA Point P(x,y) on the circle of unit radius at an obtuse angle θ > π/2 What is Sine Wave? Exaple for trigiometric function Use in Mathematics An geometric waveform that oscillates (moves up, down or side-to-side) periodically, and is defined by the function y = sin x. In other words, it is an s-shaped, smooth wave that oscillates above and below zero. The Opus palatinum de triangulis of Georg Joachim Rheticus, a student of Copernicus, was probably the first in Europe to define trigonometric functions directly in terms of right triangles instead of circles, with tables for all six trigonometric functions; this work was finished by Rheticus' student Valentin Otho in 1596. The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case does not depend on the size of the particular right triangle chosen, as long as it contains the angle A, since all such triangles are similar. Unit circle TOA tangent, opposite / adjacent
Transcript: Square Wave Sine Wave Sinusoid Smooth repetitive oscillation Applied in:Mathematics Physics Engineering Single processing Other fields. Theory behind it -Non-Sinusoidal periodic waveform -Non-sinusoidal waveforms are waveforms that are not pure sine waves but it has a function of sine waves. -Amplitude of it alternates at a stable frequency between fixed minimum and maximum value -Square waves are mostly used in Single Processing and Electronics -Start with the sine wave -We have to give it the right period -Doing a shrink by a factor of (Pi) makes the function pass through (1, 0) y=sinx The real formula Use of Square Wave - Square wave are used in generation named as relaxation oscillators. - They are used because square waves are easy to produce. - The frequency, f = 1/T , of the square-wave is independent of output voltage V-out. - A circuit that is designed to go quickly from cutoff to saturation will produce a square or rectangular wave at its output. - It is known as Rademacher function - Used sometimes for sounds in music - Instruments such as horns, trombones and saxophones Schmitt trigger Conclusion - Square Wave is used mostly in Generator - It is a easy wave to produce - They have an interesting mix of practice and theory. In practice, they are extremely simple. In their simplest form, they consist of an alternating sequence of amplitudes. However in theory, they are somewhat difficult to analyze. - They're found in numerous applications. Sources: - Thompson, A. R.; Moran, J. M.; and Swenson, G. W. Jr. Interferometry and Synthesis in Radio Astronomy. New York: Wiley, p. 203, 1986. http://mathworld.wolfram.com/SquareWave.html - Weisstein, Eric W. "Fourier Series--Square Wave." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FourierSeriesSquareWave.html - Hazewinkel, Michiel, ed. (2001), "Sinusoid", Encyclopedia of Mathematics, Springer, - Hodges, F. M. "Square Wave in Generators (2003): 175-82. Web. 18 Feb. 2010. - Epsicokhan, Jamahl. "Square wave sinusoidal." Jammer's Reviews. N.p., 20 Feb. 2004. Web. 15 Mar. 2010. Thank you! Rea Dika Nadja Gjakova Period: 2Pi Amplitude:1 Range: -1 to 1 Domain: -infinit to infinit Period: 2Pi Amplitude: 3 Domain: -infinity to infinity Range: 3,-3
Transcript: \ Destructive Interference Doppler Effect Reflection is when incoming light hits an object and bounces off. Very smooth surfaces such as mirrors reflect almost all incoming light. A surface wave is a wave in which particles of the medium undergo a circular motion Electromagnetic Spectrum Mechanical Waves 1. transverse and longitudinal 2. transverse 3. longitudinal 4. diffraction 5. refraction 6. the combination of two or more waves that results in a single wave 7. destructive interference 8. visible light 9. radio waves 10. mechanical wave The reflection of sound follows the law "angle of incidence equals angle of reflection", sometimes called the law of reflection 1. Name two types of mechanical waves 2. Which type of wave moves in an up and down motion? 3. What type of wave moves parallel to the wave energy? 4. a change in the direction of a wave when the wave finds an obstacle or an edge, such as an opening is known as: 5. the bending of a wavefront as the wavefront passes between two substances in which the speed of the wave differs is called: 6. What is Constructive Interference? 7. the combination of two or more waves that reduces or cancels the amplitude is known as: 8. the only part of the electromagnetic spectrum seen by the human eye is: 9. What are the waves used for broadcasting radio signals called? 10. a disturbance in matter that carries energy from one place to another is: the interference of two or more waves of equal frequency and phase, resulting in their mutual reinforcement and producing a single amplitude equal to the sum of the amplitudes of the individual waves. ANSWER KEY Wave Powerpoint Vassiah White & Richard Rockett Ms.Pugh 7th period the interference of two waves of equal frequency and opposite phase, resulting in their cancellation where the negative displacement of one always coincides with the positive displacement of the other. Frequency- the rate at which something occurs or is repeated over a particular period of time or in a given sample Diffraction of Waves Reflection & The Law DEFINE: diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path Electromagnetic Waves A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves QUIZ the visible spectrum makes up only a small fraction of the different types of radiation that exist. To the right of the visible spectrum, we find the types of energy that are lower in frequency than visible light. These types of energy include infrared rays, microwaves, and radio waves. These types of radiation surround us constantly, and are not harmful, because their frequencies are so low. Constructive Interference Mechanical waves are caused by a disturbance or vibration in matter, whether solid, gas, liquid, or plasma. Matter that waves are traveling through is called a medium. Refraction of Waves Electromagnetic Spectrum A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space. Transverse, Longitudinal, Surface Waves Ultrasound Electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies; this classification is known as the electromagnetic spectrum. An ultrasound scan is a medical test that uses high-frequency sound waves to capture live images from the inside of your body. Ultra-sound waves can be bounced off tissues by using special devices. The echoes are then converted into a picture called a sonogram. The Doppler effect describes the shift in the frequency of a wave sound when the wave source and/or the receiver is moving. The Doppler effect is something you're familiar with. If you hear an emergency vehicle with its siren on, you notice an abrupt change in the frequency of the siren when it goes past you. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves Pitch- the quality of a sound governed by the rate of vibrations producing it; the degree of highness or lowness of a tone
Transcript: Nobody knows babies like we do! Quality products . Good Customer service. Every Kid really loves this store.. BABYLOU ABOUT US About Us BabyLou was established in 2004. It has been more than a decade since we started, where we have ensured to take care of every need and want of every child and infant under one roof, true to the caption “NO BODY KNOWS BABIES LIKE WE DO”. Our benchmark is to provide 100% customer service and satisfaction and continue to deliver the same with a wide range of toys, garments and Baby Products. Play and Create We Are Best 01 02 03 Block games Building Blocks help Kids to use their brain. PLAY TO LEARN in Crusing Adventures Our Discoveries Enjoy a sunny vacation aboard a luxury yacht with the LEGO® Creator 3in1 31083 Cruising Adventures set. This ship has all the comforts you need, including a well-equipped cabin and a toilet. Sail away to a sunny bay and take the cool water scooter to the beach. Build a sandcastle, enjoy a picnic, go surfing or check out the cute sea creatures before you head back to the yacht for a spot of fishing. Escape into the mountains Disney Little Princes in Also available for your Babies..... Also... Out of The World… Our reponsibility BABYLOU…. Our Responsibility All children have the right to fun, creative and engaging play experiences. Play is essential because when children play, they learn. As a provider of play experiences, we must ensure that our behaviour and actions are responsible towards all children and towards our stakeholders, society and the environment. We are committed to continue earning the trust our stakeholders place in us, and we are always inspired by children to be the best we can be. Innovate for children We aim to inspire children through our unique playful learning experiences and to play an active role in making a global difference on product safety while being dedicated promoters of responsibility towards children.
Transcript: amplitude A Sine Wave is a mathematical curve that describes a smooth repetitive oscillation. Also known as a sinusoid. Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. It is applied in physics, mathematics, engineering and signal processing and many other fields. Sine waves relate to how sound is reproduced What is a Sine Wave? A sine wave can be converted into sound by a loudspeaker and will be perceived to be a steady, pure tone of a single pitch. The sounds from orchestral instruments usually consists of a fundamental and a complement of harmonics, which can be sine waves of a fundamental frequency. The process of decomposing a musical instrument sound or any other periodic function into its constituent sine or cosine waves is called Fourier analysis. You can characterize the sound wave in terms of the amplitudes of the constituent sine waves which make it up. That is how Sine Waves relate to how sound is reproduced. Fourier analysis wavelength Where are Sine Waves in Nature Sine Wave That is all folks :) Fourier analysis is the reducing of a complex wave to a combination of sine waves and is fundamental to many of the sciences, especially those involving sound and signals. Fourier analysis is central to signal processing and the analysis of time series, where seemingly random sets of data points are studied to make clear a statistical trend. Fourier analysis is also used in probability theory, where it is used to prove the central limit theorem, which helps to explain why bell curves, or normal distributions, is everywhere in nature. Sine Waves are found in Ocean waves, light waves, and electricity as well. Sine waves in electricity can be used to model the intensity of an alternating current. Sine waves in light is decomposed into sums of sine waves. Waves at the surface of the ocean are sine waves. Whenever you listen to music or play a stereo you are listening to sound waves which have the shape of sine waves. Stephanie Souza April 14, 2014
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