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The document discusses phase and phase difference for harmonic waves. It defines phase as the fraction of the wave cycle that has passed by with respect to the origin, which can be written as an expression inside the brackets of the wave function. Phase difference is the difference in phase between two points at the same time. The document provides an example wave function and practice problems calculating phase and phase difference based on the definitions and equations provided.
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1. A standing wave is formed by two waves of equal amplitude, wavelength, and frequency travelling in opposite directions in the same medium.
2. Nodes occur at positions where the amplitude is zero, while antinodes occur at positions of maximum amplitude. The distance between nodes is half the wavelength, and between a node and adjacent antinode is a quarter wavelength.
3. For a string fixed at both ends, standing waves can form with wavelengths of 2L/m, where L is the string length and m is a positive integer. The lowest frequency is called the fundamental frequency. Higher integer multiples of this frequency are the harmonics.
Fourier transform in X-ray crystallography .ppt
The Fourier transform connects the diffraction pattern of X-rays scattered by a crystal to the electron density distribution within the crystal's unit cell. The structure factors obtained from diffraction intensities represent the Fourier transform of the electron density. However, the phases of the structure factors are lost during data collection, posing the phase problem. Techniques like isomorphous replacement, multiple wavelength anomalous diffraction, and molecular replacement aim to determine the missing phase information and allow calculation of electron density maps revealing a crystal's structure.
Linear Transformations_part1.pdf
1. A linear transformation is a function between vector spaces that preserves vector addition and scalar multiplication.
2. To be a linear transformation, T(u+v) must equal T(u)+T(v) and T(αu) must equal αT(u) for any vectors u,v and scalar α.
3. Properties of linear transformations include: the zero vector maps to the zero vector; the image of a linearly independent set is linearly independent; and the image of any subspace is a subspace. The transformation is determined by its effect on a basis.
progressive wave
1) The document defines transverse and longitudinal waves, and discusses key wave parameters such as amplitude, period, frequency, wavelength, phase, and velocity.
2) It provides equations for transverse wave motion and defines related concepts like angular frequency, wave number, phase difference, and graphical representations of waves.
3) An example question is given and solved to determine the amplitude, frequency, wavelength, velocity, and propagation direction of a progressive wave defined by the equation y = 0.3 sin (5πx + 200πt).
15Waves ppt 1.pdf
This document discusses different types of mechanical waves and their properties. It defines mechanical waves as oscillations that transfer energy through a medium. Key points include:
- Mechanical waves can be transverse (perpendicular to direction of travel) or longitudinal (parallel to direction of travel).
- They transport energy through the medium and require a medium, like air or water, to propagate.
- Examples of mechanical waves include water waves, sound waves, and waves on a string or rope.
- Harmonic waves have a sinusoidal shape described by a mathematical function involving amplitude, wavelength, frequency, and phase.
geophysics_lec4.ppt
The document discusses different types of wave velocities. It explains that the phase velocity is the speed at which the phase of an individual frequency component travels, while the group velocity is the speed at which the envelope of a wave packet propagates. For surface waves, different frequencies travel at different speeds due to dispersion, with lower frequencies traveling faster than higher frequencies. This is because surface waves travel deeper at lower frequencies and seismic velocity increases with depth.
Lecture 05 mechanical waves. transverse waves.
The speed of transverse waves on a string depends only on the ratio of tension to linear mass density. Doubling the tension and halving the linear mass density results in the same ratio, so the wave speed is unchanged. The speed in the second string is 2v.
Wk 1 p7 wk 3-p8_13.1-13.3 & 14.6_oscillations & ultrasound
This document discusses oscillations and simple harmonic motion. It begins by listing learning outcomes related to oscillations, including describing examples of free and forced oscillations. It then provides definitions and equations related to simple harmonic motion, such as the defining equation a=-ω2x. Graphs of displacement, velocity, and acceleration over time for simple harmonic motion are shown. Examples of the simple pendulum and a mass on a spring are provided to illustrate simple harmonic motion. The document also discusses the kinetic and potential energy changes that occur during simple harmonic motion.
Schutz 2
This document summarizes key concepts from special relativity, including:
1) The interval between events is invariant for all observers, leading to time dilation and Lorentz contraction.
2) Hyperbolae drawn on spacetime diagrams represent events of constant interval.
3) The Lorentz transformations relate the coordinates of events between different inertial frames in motion relative to each other.
4) Phenomena like time dilation and length contraction arise from the invariance of the spacetime interval between events in different frames.
Position and time plots learning objective
This learning object aims to explore the relationship between position plots and time plots. I initially struggled to comprehend the distinction between the two plots. However, I was able to reach an understanding after some research and practice. Hopefully my learning objective can help other students gain a better understanding of this topic as well!
Physics 2_Lecture 18 to 21_Phy2_Spring 2023-24 (1).pdf
Physical Society the sentence but short speech on challenges of educational system in Bangladesh studies and sadie bahamians Horse hijabs husks jms bans bbs bbs bdb dnc dms msn hdhdhdbhdhdhdhdhdhdhdhdhdhfhdhdhdhdbdbdhdhdbdhdhdhdh
Vector calculus
1. Vector calculus deals with vector-valued functions and their derivatives. It includes vector point functions that assign vectors to points in space, as well as scalar point functions that assign real numbers.
2. Key concepts include the gradient of a scalar function, the divergence and curl of a vector function, and vector fields to describe variations of quantities like velocity over a region of space.
3. Vector calculus theorems relate integrals over surfaces to integrals over bounding curves or volumes, such as Green's theorem, Stokes' theorem, and the divergence theorem. These allow problems involving surfaces and volumes to be solved via line and surface integrals.
Standing Waves
Standing waves occur when two waves of equal amplitude, frequency, and wavelength travel in opposite directions and combine. When this happens, the result is a wave that oscillates in simple harmonic motion where the string moves only up and down. Nodes occur where the amplitude is zero and anti-nodes where it is maximum. Standing waves can form on a string with fixed ends, with wavelengths that are integer divisions of the string length and resonant frequencies dependent on tension and mass density. This principle applies to stringed musical instruments where the string forms standing waves at harmonic frequencies.
Harmonic wave physics
The document defines key terms related to harmonic waves such as amplitude, wavelength, wavenumber, and wave speed. It explains that wavelength is the shortest distance a wave repeats itself and relates wavenumber to wavelength using the equation k=2π/λ. The document also presents the wave speed equation V=λf and uses graphs of two radio waves with different periods to calculate their frequencies, wavelengths, and velocities. It determines that radio wave 2 has a higher velocity than radio wave 1.
Group velocity and phase velocity
The document discusses phase and group velocity of waves. It defines phase velocity as the velocity at which the phase of any single frequency component travels, represented by the crests of a wave. Group velocity is defined as the velocity at which the envelope or outline of a wave packet travels through space. The document demonstrates through equations and diagrams that for wave packets formed from superimposed waves, the phase velocity can be greater than the group velocity.
Harmonic Waves
A harmonic wave is a wave that undergoes simple harmonic motion as it travels. It can be described by the equation D(x,t)=Asin(kx-wt+φ), where D is displacement, A is amplitude, k is wave number, w is angular frequency, x is position, t is time, and φ is phase. The document provides examples of how to use this equation to calculate properties like wavelength, frequency, and acceleration of a harmonic wave traveling through different media. It also includes sample problems solving for these wave properties given values for variables like velocity, frequency, amplitude, and position over time.
KRK-PhysicsofUltrasound.pptx
Ultrasound propagates as pressure waves through materials. The speed of sound depends on the density and compressibility of the medium. Plane and spherical waves can model ultrasound propagation. Reflection, refraction, and attenuation occur at boundaries between tissues. The Doppler effect alters ultrasound frequency based on relative motion between the source and receiver. Beamforming uses an array of transducer elements to focus ultrasound and form images by detecting echoes from tissue interfaces and structures.
derivation of Wave equation
This document discusses the wave equation and properties of one-dimensional waves. It begins by defining the wave equation as a hyperbolic partial differential equation. It then derives the one-dimensional wave equation mathematically by taking the double derivatives of a wave function with respect to position and time. The key result is that the second derivative of the wave function with respect to position equals the inverse velocity squared times the second derivative with respect to time. It then discusses the differences between traveling waves, which transport energy and move crests/troughs, and standing waves, which remain in a fixed position with nodes and antinodes.
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Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Wound healing PPT
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A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
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Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
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Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
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Learning object 3
- 1. Physics 101-Learning Object Phase and Phase Difference
- 2. Phase • The wave function of a harmonic wave can be written as: D(x,t) = Asin (kx-ωt+ɸ) when it is travelling in the direction of increasing x (position along the string) , and can be written as D(x,t) = Asin (kx+ωt+ɸ) when it is travelling in the direction of decreasing x. • The phase of a harmonic wave is designated by the Greek letter phi, ɸ and is measured in radians. The phase, which is dependent on position and time, is the fraction of the wave cycle that has passed by with respect to the origin. • The phase is the expression inside the brackets of the wave function of a harmonic wave (x,t), therefore the phase can be written as: ɸ (x,t) = kx+ωt+ɸ • NOTE: DO NOT CONFUSE PHASE, ɸ, WITH PHASE CONSTANT, ɸ.
- 3. Phase Difference • The phase difference of a harmonic wave is designated by Δɸ and is measured in radians. The phase difference is the difference between the phase at two separate points (x₁ and x₂), at the same time. Therefore: Δɸ = phase of wave at x₂ - phase if wave at x₁ = (kx₂-ωt+ɸ) - (kx₁-ωt+ɸ) = k (x₂ - x₁) = kΔx = 2π(Δx/λ), where λ is the wavelength
- 4. Practice Questions • The wave function of a harmonic wave is given by the function D(x,t) = (0.5m)sin (4x-2t+(π/2)), 1) what is the expression for the phase of this wave? 2) what is the phase when t=3sec and x=2m? 3) if the difference between two points is λ/6, what is the phase difference?
- 5. Solutions • Answers: 1) Phase = 4x-2t+(π/2) 2) Phase = 4(2)-2(3)+(π/2) = 3.57 rad 3) Phase difference = 2π(Δx/λ) = 2π((λ/6)/λ) = π/3