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1. The document discusses constructive and destructive interference that occurs when two waves meet at a point. 2. For constructive interference to occur, the path length difference (Δd) between the waves must be an integer multiple of the wavelength. For destructive interference, Δd must be a half-integer multiple of the wavelength. 3. The document uses examples of waves that are in-phase or out-of-phase to show how the equations for Δd change depending on whether the interference is constructive or destructive.

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Lo1

This document discusses the derivation of the formula for wave speed on a string. It begins by isolating a small segment of string at the peak of a pulse. The formula for wave speed is then given as v=√(Ts/μ), where Ts is the tension force on the segment and μ is the linear mass density of the string. The document then defines linear mass density as the mass per unit length and tension force as the restoring force pulling the string segment inward. Through applying Newton's second law to the segment, the formula is derived. Examples are then given to show how wave speed is affected by changes in tension or mass density.

Standing waves lo

A standing wave is formed by two harmonic waves of equal amplitude, wavelength and frequency moving in opposite directions. When they collide, each segment of the string oscillates in simple harmonic motion (SHM). Nodes occur where the amplitude is zero, and antinodes occur where the amplitude is at a maximum of 2A. The fundamental frequency is the lowest frequency at which a string will oscillate, and higher harmonics are integer multiples of this frequency. Standing waves in instruments like flutes and guitars are responsible for producing musical notes. The document provides an example of calculating the wave speed, length, and first three harmonic frequencies of a guitar string with given properties.

Standing waves

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.

Standing waves on Strings

This document discusses standing waves on strings. It defines key terms like nodes and antinodes. The fundamental frequency is the lowest frequency for a string of length L, and is determined by the longest wavelength of λ=2L. Examples are given to calculate the wave speed, number of reflections in a time period, and frequencies of different harmonics. The fundamental frequency is directly proportional to the square root of the tension and inversely proportional to the length and square root of the linear mass density. Decreasing the tension decreases the fundamental frequency.

Lo 5: Interference of Waves in a Pond

- A pebble was dropped in a pond, generating a wave with an amplitude of 1.0 cm and a phase constant of π.
- A second identical pebble was dropped, generating interference between the two waves.
- Given the amplitude of the resultant wave is 1.3 cm, the phase constant difference between the waves is calculated to be 1.7264 radians.
- The phase constant of the resultant wave at t=2.0 seconds is therefore 2.3 radians.

Lo 2

This document defines and explains standing waves. A standing wave results from two identical waves traveling in opposite directions with the same frequency. When the frequency is resonant, the waves will superimpose to form a stationary pattern with antinodes of maximum displacement and nodes of zero displacement. The position of nodes and antinodes can be determined using the standing wave equation. For a guitar string example, the document calculates the amplitude and wavelength of the traveling wave, finds the positions of the first two nodes, and determines the first harmonic frequency.

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.

Standing waves

Standing waves are harmonic waves with equal amplitude, wavelength, and frequency that are moving in opposite directions. They have a phase constant of 0. Standing waves have nodes where the amplitude is 0 and antinodes where the amplitude is at a maximum of 2A. The distance between nodes is half the wavelength, as is the distance between antinodes. An example problem calculates the length of a water pipe with a standing wave pattern by determining the wavelength from the given frequency and speed, and using the node and antinode spacing to relate the length to the wavelength.

Standing wave lo5

This document discusses standing waves, which are formed by the superposition of two waves traveling in opposite directions with the same amplitude, wavelength, and frequency. It defines nodes as points of zero amplitude and antinodes as points of maximum amplitude. Equations are provided for calculating the position of nodes and antinodes. An example problem demonstrates using these equations to find the location of the first node and antinode for a given wave function.

Fisika dasar 2 prodi fisika 2-glb1

This document provides an overview of the course "Basic Physics II" taught by Mukhtar Effendi. It lists the main topics to be covered, including mechanical waves, static electricity, electromagnetism, oscillatory circuits, and electromagnetic waves. Formulas for wave propagation, interference, and Maxwell's equations are presented. Examples of solving wave equations and calculating wave properties such as amplitude, wavelength, frequency and speed are also provided.

4 wave speed

This document discusses wave speed and the relationship between speed, frequency, and wavelength of waves. It states that the speed of a wave is equal to the frequency multiplied by the wavelength, and provides the equation v = fλ. It then gives examples of using this equation to calculate speed, frequency, or wavelength when two of the three values are known.

Physics 101 Learning Object #7 Interference of Waves and Beats

The document discusses various topics relating to interference of waves including constructive and destructive interference, beats, and provides examples of problems relating to these topics. It explains the conditions needed for constructive and destructive interference and how beats occur due to two waves with slightly different frequencies combining to produce a sound that varies in amplitude over time. Several example problems are worked through applying the concepts of interference and beats.

Standwaves

This LO gives you a simple easy to understand explanation of what a standing wave is (video included) and how it is different from a travelling wave. Afterwards a few sample questions are given to apply knowledge.

Physics LO 4

This document summarizes key concepts about sound waves, including:
1) Sound waves are longitudinal waves that cause alternating high and low pressure areas as molecules are displaced in the propagation direction.
2) The speed of sound depends on the medium and can be calculated using the bulk modulus and density.
3) Sound waves can be described by displacement, pressure, wavelength, frequency, and other variables, with displacement and pressure 90 degrees out of phase.

Waves

Progressive waves transfer energy through a medium by vibrating particles in the medium. There are two main types of waves: longitudinal waves where particles vibrate parallel to the wave direction, and transverse waves where particles vibrate perpendicular to the wave direction. The speed of a wave can be calculated using the formula that the speed equals the wavelength multiplied by the frequency.

Standing Waves On a String

A string fixed at both ends has normal modes of vibration that are standing waves. The wavelength of each normal mode is given by λm= 2L/m, where L is the length of the string and m is a positive integer. The longest wavelength, or fundamental frequency, corresponds to m=1. Higher values of m correspond to shorter wavelengths and higher frequencies. The frequencies of the normal modes, or harmonics, are directly proportional to m.

Learning Object- Standing Waves on Strings

This is my learning object about standing waves on a string. I talk about the harmonics, the equation for calculating the frequency for a wave on a string, and gave an example problem.

Learning object 6

The document discusses wave properties of a string with a tension of 80N, linear mass density of 2 kg/m, and length of 0.3m. It is determined that:
1) The wave speed is 6.32 m/s.
2) If n=6, the wavelength is 0.1m.
3) For the fundamental frequency to increase by 10Hz, the tension must increase, as the wave speed depends on the square root of tension over linear density.
4) For a 10Hz increase in fundamental frequency, the tension needs to increase by 223N.

Physics learning object 3

Harmonic Waves (up to but not including Travelling waves) and shows the formulas associated with the topic, as well as definition and examples. In the form of a pdf.

Standing waves

A standing wave is a vibration where some points in a medium remain fixed while other points vibrate at maximum amplitude, with points of zero displacement called nodes. The formula for a standing wave on a string relates the length of the string, number of antinodes, and wavelength. For a 2 meter string vibrating at its first harmonic with 55 cycles in 10 seconds, the frequency is 5.5 Hz, period is 0.18 seconds, wavelength is 4 meters, and speed is 22 meters per second.

Lo1

Lo1

Standing waves lo

Standing waves lo

Standing waves

Standing waves

Standing waves on Strings

Standing waves on Strings

Lo 5: Interference of Waves in a Pond

Lo 5: Interference of Waves in a Pond

Lo 2

Lo 2

Standing Waves

Standing Waves

Standing waves

Standing waves

Standing wave lo5

Standing wave lo5

Fisika dasar 2 prodi fisika 2-glb1

Fisika dasar 2 prodi fisika 2-glb1

4 wave speed

4 wave speed

Physics 101 Learning Object #7 Interference of Waves and Beats

Physics 101 Learning Object #7 Interference of Waves and Beats

Standwaves

Standwaves

Physics LO 4

Physics LO 4

Waves

Waves

Standing Waves On a String

Standing Waves On a String

Learning Object- Standing Waves on Strings

Learning Object- Standing Waves on Strings

Learning object 6

Learning object 6

Physics learning object 3

Physics learning object 3

Standing waves

Standing waves

Quantum superposition | Overview

Quantum mechanics describes quantum states that can exist in superposition, where an element can exist in multiple states simultaneously. When measured, the element collapses into a single definite state. Quantum computing uses this principle of superposition, where qubits can represent 0 and 1 simultaneously, allowing massive parallelism that exceeds classical computers.

1.5 interference - Interferens Fizik SPM

1. The document discusses the principles of interference and superposition of waves. It describes how two waves can interfere constructively or destructively depending on whether their crests and troughs coincide or cancel each other out.
2. Experiments are described to investigate the interference patterns of water waves. It is shown that the distance between nodes increases with increasing wavelength and decreasing separation between the two sources.
3. Young's double-slit experiment is explained as demonstrating the interference of light waves. Light passing through two slits acts as two coherent sources, producing an interference pattern of bright and dark fringes on a screen.

superposition theorem

This document discusses the superposition theorem for electrical circuits. The superposition theorem states that the response in any branch of a linear circuit with multiple independent sources is equal to the sum of the responses from each source acting alone. It works by replacing all other sources with their internal impedances (short circuits for voltage sources, open circuits for current sources) and calculating the contribution of each source individually. The superposition theorem is important for circuit analysis and is used to convert circuits into equivalent Norton or Thevenin circuits. It applies to linear networks containing independent sources, linear dependent sources, resistors, inductors, and capacitors.

Superposition Principle in Electric Circuit Fundamentals and Electrical Engin...

Superposition principle is an important theorem in Electric Circuit fundamentals, It involves the calculation of current and voltage contributions separately from all sources in any circuit and then to sum up all these values for calculating overall voltage and current effects on any resistor or component. Superposition theorem is an important theorem which relieves problem of solving complex simultaneous problems. While, apply principle to any circuit, current sources are made open, whereas voltage sources are suppressed to short circuit.

Medical Uses Of Ultrasound

Medical uses of ultrasound can include imaging the inside of the body and detecting blood flow. Bats and dolphins use echolocation with ultrasound to navigate. We can apply this principle to medical ultrasound imaging by emitting ultrasound pulses and mapping the echoes to visualize internal structures. Doppler ultrasound further analyzes the ultrasound echoes to determine blood flow velocity within the body. While 2D ultrasound is considered safe for imaging fetuses, more advanced 4D ultrasound using higher energies requires further consideration regarding any potential risks from heating effects.

Applications of Ultrasound in Medicine

Ultrasound uses high-frequency sound waves to produce images of internal organs and structures. It has many medical applications. Ultrasound works by sending pulses of sound into the body that bounce off tissues and create echoes. These echoes are converted into electrical signals and processed to form images. The images provide information about anatomy, abnormal growths, and blood flow.

Superposition theorem

The superposition theorem allows the analysis of circuits with multiple sources by considering each source independently and adding their effects. It can be applied when circuit elements are linear and bilateral. To use it, all ideal voltage sources except one are short circuited and all ideal current sources except one are open circuited. Dependent sources are left intact. This allows the circuit to be solved for each source individually and the results combined through superposition. Examples demonstrate finding currents through specific elements in circuits with multiple independent and dependent sources. A limitation is that superposition cannot be used to determine total power due to power being related to current squared.

Network Theorems.ppt

This document introduces several important network theorems: superposition, Thevenin's, Norton's, maximum power transfer, Millman's, substitution, and reciprocity. It provides definitions and procedures for applying each theorem, such as replacing network elements with voltage/current sources and determining equivalent resistances and voltages. The theorems allow analyzing complex networks, determining outputs when components change, and maximizing power transfer between networks.

Quantum superposition | Overview

Quantum superposition | Overview

1.5 interference - Interferens Fizik SPM

1.5 interference - Interferens Fizik SPM

superposition theorem

superposition theorem

Superposition Principle in Electric Circuit Fundamentals and Electrical Engin...

Superposition Principle in Electric Circuit Fundamentals and Electrical Engin...

Medical Uses Of Ultrasound

Medical Uses Of Ultrasound

Applications of Ultrasound in Medicine

Applications of Ultrasound in Medicine

Superposition theorem

Superposition theorem

Network Theorems.ppt

Network Theorems.ppt

2D wave interference

This document discusses two-dimensional interference patterns that arise when waves propagate in different directions. It explains that constructive interference occurs when the path difference between two waves is an integer multiple of the wavelength, causing the amplitudes to add. Destructive interference happens when the path difference is a half-integer multiple of the wavelength, reducing the amplitude. Formulas are provided for calculating the conditions of constructive and destructive interference between two waves.

Interference of light waves

Interference of light refers to the redistribution of light energy due to superposition of two light waves. This superposition leads to a pattern of alternate dark and bright fringes. These dark and bright fringes are called as minima and maxima respectively.

6.wave_optics_1.ppt

1. The document discusses key concepts in wave optics including wavefronts, Huygens' principle, and refraction of light using Huygens' principle.
2. Huygens' principle states that each point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the envelope of all the secondary wavelets.
3. Refraction is explained using Huygens' principle, where the refracted wavefront is the envelope of secondary wavelets emerging from the incident wavefront after passing through the interface between two media.

Chapter 4a interference

When two light waves pass through the same point in space simultaneously, interference occurs. Constructive interference happens when the waves are in phase and add to produce a larger wave, while destructive interference occurs when they are out of phase and cancel each other out. The intensity of the resulting interference pattern depends on the phase difference between the waves. In a double slit experiment, the phase difference and resulting interference is determined by the path length difference between waves passing through each slit.

Lo9 by fei H

Thomas Young's double slit experiment demonstrates the principles of interference effects in light waves. Light passing through two slits will produce interference patterns on a screen due to differences in the path lengths traveled by each wave. The conditions for constructive and destructive interference depend on the path length difference being equal to whole number or half-number multiples of the wavelength. Measuring the spacing of bright or dark bands allows the wavelength of monochromatic light to be calculated indirectly, even when the slit separation is much smaller than the screen distance.

Interference of 2D waves

Two waves originating from distinct sources can interfere constructively or destructively. Constructive interference occurs when the waves are in phase, meaning the peaks and troughs of each wave align. This results in an interference pattern where the displacement is an integer multiple of the wavelength. Destructive interference happens when the waves are out of phase, so the peaks of one wave align with the troughs of the other. In this case, the displacement is an integer plus half the wavelength. The document provides equations and examples to describe the conditions for constructive and destructive interference between two waves.

Superposition 2008 prelim_solutions

1. When two waves meet at a point in space, their amplitudes add vectorially. Constructive interference occurs when the path difference is an integral multiple of the wavelength, producing loud sounds. Destructive interference occurs when the path difference is an odd multiple of half the wavelength, producing soft sounds.
2. As frequency increases, wavelength decreases. This causes the positions of constructive and destructive interference to shift towards the central axis as the microphone passes through them.
3. Increasing the slit separation in a double-slit experiment doubles the fringe separation in the interference pattern. The slit width does not affect fringe separation but decreases intensity.

Double-Slit Interference

This PowerPoint summarizes double-slit interference by transforming the interference patterns formed by Young's experiment into a right triangle. It is an attempt to clarify the significance of all of its components in order to determine different angles of which bright fringes appear on a screen L distance away from the two slits and eventually to conceptualize the distance between bright fringes by knowing the value of the wavelength of light.

Interference

This document discusses wave interference patterns produced by two point sources of waves. It explains that when two waves are perfectly in phase, constructive interference occurs, shown as circular wave fronts. The points of constructive and destructive interference can be determined mathematically based on the path difference between the sources being equal to integer multiples of the wavelength. As an example, it analyzes the interference pattern between two boats emitting waves 80m apart, finding the point of constructive interference occurs at x = -8.90995 due to the symmetry of the setup.

Physics Learning Object 6

A standing wave is formed by two traveling waves moving in opposite directions with the same amplitude, wavelength, and frequency. The superposition of these waves results in locations of maximum and minimum displacement known as anti-nodes and nodes. The equation for a standing wave is the sum of the equations for the two traveling waves. This creates a stationary wave pattern with anti-nodes at locations of maximum displacement and nodes at locations of no displacement.

Chapter 3 wave_optics

The document discusses wave optics and electromagnetic waves. It defines key concepts like wavefronts, which connect points of equal phase, and rays, which describe the direction of wave propagation perpendicular to wavefronts. It explains Huygens' principle, which states that each point on a wavefront acts as a secondary source of spherical wavelets to determine the new wavefront position. The principle of superposition states that multiple waves add linearly at each point in space to determine the resulting disturbance. Interference occurs when waves are out of phase and their amplitudes diminish or vanish.

Lo7

Constructive and destructive interference occur when waves meet. Constructive interference happens when waves are in phase, amplifying the combined effect. Destructive interference occurs when waves are out of phase, canceling each other out temporarily. For interference to happen, the path difference between waves must be an integer multiple of the wavelength for constructive interference or an integer plus half a wavelength for destructive interference.

Physics 101 Huygens' Principle and Interference

Huygens' principle states that each point on a wavefront can be seen as a source of secondary wavelets. The interference of these wavelets determines the shape of subsequent wavefronts as the wave propagates. Interference occurs when two waves superimpose, resulting in areas of constructive and destructive interference where wave amplitudes add or cancel. Constructive interference occurs when the path difference between waves is an integer multiple of the wavelength, while destructive interference requires an odd integer multiple. Beats are heard when tones of similar frequencies interfere, with the beat frequency equal to the difference between the frequencies.

2. interference

#INTERFERENCE presentation
#LASER and optics
#Physics
#Presentation
#Education
#Teaching
#Knowledge
#technology

Ch16 ssm

1. The document provides conceptual problems and solutions related to superposition and standing waves. It discusses topics like wave pulses traveling in opposite directions, fundamental frequencies of open and closed organ pipes, and using resonance frequencies to estimate air temperature.
2. It also covers problems involving interference of two waves with different phases and frequencies, and deriving an expression for the envelope of a superposed wave.
3. For one problem, it plots the total displacement of a superposed wave at t=0, and the envelope function at t=0, 5, and 10 seconds. From these plots, it estimates the speed of the envelope and compares it to the theoretical value obtained from the problem parameters.

Lo7

Waves can interfere constructively or destructively when they meet. Constructive interference occurs when waves are in phase and their amplitudes add, increasing the net amplitude. Destructive interference occurs when waves are out of phase and their amplitudes cancel out. For interference to occur, the path length difference between waves must be an integer multiple of the wavelength. Spherical waves spread out from their source and decrease in amplitude with distance.

Physics learning object 2

This learning object is based on 2-D interference and beats. It addresses important concepts behind these two ideas and includes a few quantitative problems.

Interference (15.5)

When two or more electromagnetic waves combine, they form a resultant wave through interference. Constructive interference occurs when waves are in phase, amplifying the total wave. Destructive interference occurs when waves are out of phase, reducing the total wave. The amount of phase difference depends on the path difference between waves - an integer multiple of the wavelength leads to constructive interference, while half-integer multiples lead to destructive interference.

Interference

The document discusses interference and thin film interference. Some key points:
- Interference occurs when light waves combine, and conditions for interference require coherent light sources that maintain a constant phase relationship.
- Thin film interference is observed when light reflects or transmits through a thin film. It results from the optical path difference between light rays that undergo different numbers of reflections within the film.
- Interference patterns in thin films depend on factors like the film thickness, wavelength of light, and angle of incidence. This allows properties like wavelength and refractive index to be measured from analysis of the interference fringe patterns.

Quantum Mechanics Part-2_1701531359799.pptx

Wave velocity or phase velocity is the velocity with which a monochromatic wave propagates through a medium. It is represented by Vp and is equal to the ratio of the angular frequency (ω) to the wave number (k). The phase velocity describes the velocity at which the phase of the wave propagates in space, not the velocity of energy transport.

2D wave interference

2D wave interference

Interference of light waves

Interference of light waves

6.wave_optics_1.ppt

6.wave_optics_1.ppt

Chapter 4a interference

Chapter 4a interference

Lo9 by fei H

Lo9 by fei H

Interference of 2D waves

Interference of 2D waves

Superposition 2008 prelim_solutions

Superposition 2008 prelim_solutions

Double-Slit Interference

Double-Slit Interference

Interference

Interference

Physics Learning Object 6

Physics Learning Object 6

Chapter 3 wave_optics

Chapter 3 wave_optics

Lo7

Lo7

Physics 101 Huygens' Principle and Interference

Physics 101 Huygens' Principle and Interference

2. interference

2. interference

Ch16 ssm

Ch16 ssm

Lo7

Lo7

Physics learning object 2

Physics learning object 2

Interference (15.5)

Interference (15.5)

Interference

Interference

Quantum Mechanics Part-2_1701531359799.pptx

Quantum Mechanics Part-2_1701531359799.pptx

C# Interview Questions PDF By ScholarHat.pdf

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A beginner’s guide to project reviews - everything you wanted to know but wer...

A beginner’s guide to project reviews - everything you wanted to know but wer...Association for Project Management

APM event held on 9 July in Bristol.
Speaker: Roy Millard
The SWWE Regional Network were very pleased to welcome back to Bristol Roy Millard, of APM’s Assurance Interest Group on 9 July 2024, to talk about project reviews and hopefully answer all your questions.
Roy outlined his extensive career and his experience in setting up the APM’s Assurance Specific Interest Group, as they were known then.
Using Mentimeter, he asked a number of questions of the audience about their experience of project reviews and what they wanted to know.
Roy discussed what a project review was and examined a number of definitions, including APM’s Bok: “Project reviews take place throughout the project life cycle to check the likely or actual achievement of the objectives specified in the project management plan”
Why do we do project reviews? Different stakeholders will have different views about this, but usually it is about providing confidence that the project will deliver the expected outputs and benefits, that it is under control.
There are many types of project reviews, including peer reviews, internal audit, National Audit Office, IPA, etc.
Roy discussed the principles behind the Three Lines of Defence Model:, First line looks at management controls, policies, procedures, Second line at compliance, such as Gate reviews, QA, to check that controls are being followed, and third Line is independent external reviews for the organisations Board, such as Internal Audit or NAO audit.
Factors which affect project reviews include the scope, level of independence, customer of the review, team composition and time.
Project Audits are a special type of project review. They are generally more independent, formal with clear processes and audit trails, with a greater emphasis on compliance. Project reviews are generally more flexible and informal, but should be evidence based and have some level of independence.
Roy looked at 2 examples of where reviews went wrong, London Underground Sub-Surface Upgrade signalling contract, and London’s Garden Bridge. The former had poor 3 lines of defence, no internal audit and weak procurement skills, the latter was a Boris Johnson vanity project with no proper governance due to Johnson’s pressure and interference.
Roy discussed the principles of assurance reviews from APM’s Guide to Integrated Assurance (Free to Members), which include: independence, accountability, risk based, and impact, etc
Human factors are important in project reviews. The skills and knowledge of the review team, building trust with the project team to avoid defensiveness, body language, and team dynamics, which can only be assessed face to face, active listening, flexibility and objectively.
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Lecture_Notes_Unit4_Chapter_8_9_10_RDBMS for the students affiliated by alaga...

Title: Relational Database Management System Concepts(RDBMS)
Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : DATA INTEGRITY, CREATING AND MAINTAINING A TABLE AND INDEX
Sub-Topic :
Data Integrity,Types of Integrity, Integrity Constraints, Primary Key, Foreign key, unique key, self referential integrity,
creating and maintain a table, Modifying a table, alter a table, Deleting a table
Create an Index, Alter Index, Drop Index, Function based index, obtaining information about index, Difference between ROWID and ROWNUM
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.
Feedback and Contact Information:
Your feedback is valuable! For any queries or suggestions, please contact muruganjit@agacollege.in

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- 1. Exploring Interference By: Eugenie Kwong Learning Object 7 PHYS 101-202 Section LC2
- 2. Interference Constructive Destructive How can we determine WHERE these interferences occur mathematically? First, let us consider 2 waves that are in phase over the next two slides.
- 3. To have constructive interference, either: 1. The waves meet at a point when they are both at the greatest positive amplitude. OR 2. The waves meet a point when they are both at the greatest negative amplitude. Since we are considering 2 waves that are in phase (such as the diagram above), the waves will constructively meet up only when there is an integer number of λ between each source and the point (in order for the waves to meet up at the peaks). So if d is the path length from a source to the point where the two waves meet, then for the 2 sources, ∆d=nλ, where n is any integer (…-1,0,1,2…)
- 4. To have destructive interference: The waves meet at a point when one is at the greatest positive amplitude, while the other wave is at the greatest negative amplitude. Since we are considering two waves that are in phase with each other, the only way that the two waves will meet up in that configuration is when: - One of the waves has a path length of d1=λn - Other wave has a path length that is d2=(0.5λ+nλ)=(0.5+n)λ. (where n is any integer) Thus, ∆d=(n+0.5)λ
- 5. Concept tester: Which type of interference is at A? The speed at which the wave travels is 420m/s, and the frequency is 210Hz. The waves are in phase, and both sources emit the same type of wave.
- 6. 1. From the given information, we want to find whether or not the path length difference (∆d) agrees with the equation for constructive or destructive interference. Constructive: ∆d=nλ Destructive: ∆d=(n+0.5)λ 2. We know that d1=10m, and d2=13m, so ∆d=13m-10m=3m Given frequency and velocity, we can find the wavelength using v=fλ. λ=v/f λ=420(m/s)/210(Hz) λ=2 m 3. Now substitute into either the constructive or destructive equations for ∆d, and we find: For constructive: 3=n(2), n=1.5 is not an integer. For destructive: 3=(n+0.5)(2), n=1, which is an integer. Therefore, the interference at point A is destructive. Another way to solve this problem is to compare the individual path lengths. 10 is an integer of the wavelength 2, and 13 is a half integer multiple of the wavelength 2. This satisfies the conditions for destructive interference.
- 7. What if the two waves interfering are OUT OF PHASE? How does this affect our calculation? Let’s take a look at a simple situation:
- 8. If the second wave is rad out of phase, then this would result in ∆d having an extra rad as well. So from the original ∆d which was constructive (∆d=nλ), we add the extra phase shift term, which makes it ∆d=nλ+ . Since rad=half a wavelength, then ∆d=nλ+0.5λ =λ(n+0.5) And this corresponds to the path length difference equation for destructive interference! In general, if there is a phase shift between the two waves, then we add the phase shift to the original ∆d equation.
- 9. Concept tester: Which type of interference is at A if the two point sources are /2 radians out of phase? The speed at which the wave travels is 420m/s, and the frequency is 210Hz. The waves are in phase, and both sources emit the same type of wave.
- 10. /2 radians out of phase situation 1. Put this phase shift in terms of λ. Since λ=2 , then =λ/2 and so the waves will be (λ/2)/2 = λ/4 out of phase. 2. Add this phase shift to the original ∆d equation: ∆d=13-10+(λ/4) =3+(λ/4) =3+(2/4) =3.5 3. Compare ∆d=3.5 with the ∆d for constructive and destructive equations. Constructive: ∆d=nλ Destructive: ∆d=(n+0.5)λ 3.5 is not an integer multiple of λ=2m, therefore not constructive. If you plug in 3.5 into the destructive equation, n=6.5 which is not an integer and therefore is not destructive. (What we know from the given info: λ=2) Conclusion: the interference would be somewhere between constructive and destructive.