Physics I Oscillations And Waves
Arnt Inge Vistnes is an Associate Professor in the Department of Physics, University of Oslo, Norway, which holds a unique position in the use of numerical methods within physics education. Dr. Vistnes was the first in the department to start using numerical methods on basic physics bachelor courses, in 1997, and accordingly has long experience in the ways in which numerical methods can improve understanding of physics. He has an excellent reputation for his teaching ability and has won several prizes for good teaching. Dr. Vistnes first wrote Oscillation and Wave Physics in Norwegian to meet the need for a textbook suitable for fourth semester physics bachelor students. He has subsequently improved and added to the text and is personally responsible for most of the more than 250 illustrations in the book.
Physics I Oscillations and Waves
Your students probably know oscillations and waves when they see (or hear!) them, and we can rather easily build a formal physical model on this intuitive understanding. The resources on this page will help your students understand oscillations and waves in terms of energy and develop facility with the basic concepts we use to describe these phenomena.
Back to the giant water balloon for a rather more exciting demonstration of constructive interference. Multiple people along the perimeter of the balloon simultaneously create waves that travel inward; these add at the center to launch a small stuffed animal placed there!
Introduction to Oscillations and Waves covers the basic mathematics and physics of oscillatory and wave phenomena. By the end of the course, students should be able to explain why oscillations appear in many near equilibrium systems, the various mathematical properties of those oscillations in various contexts, how oscillations and waves are related, and the basic mathematical description and properties of a wave.
Phenomena that repeat over regular intervals of time and space play a fundamental role in many areas of physics and its applications. This course begins with a review of periodic oscillations of a simple harmonic oscillator, and proceeds to a discussion of a damped, driven, linear oscillator. Both mechanical and electrical oscillators will be discussed within a single mathematical framework. The course then turns to waves, including mechanical waves in solid, liquid, or gas media as well as electromagnetic waves. Classes of waves are distinguished, such as longitudinal and transverse as well as traveling and standing. General wave phenomena are discussed, including superposition, interference, and diffraction. Discussion of ray optics as a limiting case of wave optics leads to a simple description of reflection and refraction at plane and curved interfaces and to an understanding of simple optical instruments as well as the eye. The laboratory experiments on oscillations, mechanical waves and optics provide hands-on experience of the concepts discussed in the rest of the course. Optional topics include coupled oscillators and normal modes using matrix methods, and Fourier series and Fourier Transforms as tools for examining arbitrary signals and waves in terms of their harmonic components. Four hours of lectures and discussion and one three-hour laboratory per week.
For majors in engineering (including bio-, civil, and environmental engineering), computer and information science, physics, earth and atmospheric science, and other physical and biological sciences who wish to understand the oscillation, wave, and quantum phenomena behind everyday experiences and modern technology including scientific/medical instrumentation. Covers the physics of oscillations and wave phenomena, including driven oscillations and resonance, mechanical waves, sound waves, electromagnetic waves, standing waves, Doppler effect, polarization, wave reflection and transmission, interference, diffraction, geometric optics and optical instruments, wave properties of particles, particles in potential wells, light emission and absorption, and quantum tunneling. With applications to phenomena and measurement technologies in engineering, the physical sciences, and biological sciences. Some familiarity with differential equations, complex representation of sinusoids, and Fourier analysis is desirable but not essential. As with PHYS 1112 and PHYS 2213, pre-class preparation involves reading notes and/or watching videos, and in-class activities focus on problem solving, demonstrations, and applications.
Transverse Waves: The particle motion in this wave is perpendicular to the direction of energy propagation(transfer). The particles in this wave are oscillating up and down while the energy is propagated perpendicularly. It is important to note that a larger amplitude denotes greater energy. Electromagnetic waves and shallow water waves are both transverse waves.
Longitudinal Waves: The particle motion in this wave is parallel to the direction of energy transfer. It is key to note that the energy and particles move in the same direction. All sound waves are longitudinal waves. *It is important to note that sound waves graphs can look similar to transverse waves but they are always longitudinal*.
Standing Waves: Standing waves are formed when 2 waves travel towards each other(eg. incidental or reflected) with the same speed and similar amplitude as energy can be lost. The wavelength is the same and there is no net energy propagation. Standing waves have particles which remain stationary called nodes. The average speed of each particle is not the same at one cycle. The anti-node will be the fastest as it travels the farthest in one cycle. The distance between adjacent nodes or anti-nodes is half a wavelength. Microwaves are an example of standing wave. In a microwave, standing waves are established which is why a turntable is necessary.
There are different wavelengths that transverse waves travel at. The spectrum of different wavelengths have been divided into different sections. They are commonly given the following names (in order of increasing frequency and decreasing wavelength).
Going down the original list, frequency decreases and wavelength increases (because since v=λƒ and c remains constant). The amount of 'energy' in the waves decreases down the list, which is why X-rays are dangerous, and radio waves aren't.
Electromagnetic waves are usually defined by their wavelength in a vacuum (which seems rather silly, since frequency never changes, frequency and is what defines the characteristics (i.e. color)) but who am I to argue.
Longitudinal waves travel in one dimension, and so when they strike a boundary, they willbe reflected back in the same direction, though the will experience a phase change (i.e. when a compression hits the boundary, a rarefaction is emitted back from it, and vice versa.
This also applies to standing waves travelling in a stretched string. If both ends are connected to a boundary, then nodes (points where the string doesn't move up and down) will occur at both ends, and a number of antinodes will occur through the string, separated by nodes.
Whenever a wave is reflected from a boundary, the angle of reflection will equal the angle of incidence. Thus, if the wave strikes the boundary at 90, then it will be reflected straightback, but other angles will reflect the waves away from the source.
When two waves are moving in the same medium, the displacements of the particles add together. It is therefore possible for two waves to produce one wave of larger amplitude, or to produce two waves where the total amplitude is zero. Note, the waves and energies are still there, it's just that the two waves are adding to zero.
Principle of Superposition: The principle of superposition states that the resulting displacement of the interference between 2 waves is the algebraic sum of the displacement of each wave. Principle of superposition describes the combination of overlapping waves or wave interference.
Beats: The constructive or destructive interference of 2 waves. Beats is the change in amplitude in soundwaves. The beats can heard when the sound goes from loud to quiet to loud or when it goes from quiet to loud to quiet.
Doppler Effect: The apparent change in a wave's frequency and the wavelength due to the relative motion between the source and the observer. If a wave is blue shifted, the electromagnetic waves are getting shorter. If a wave is red shifted, the electromagnetic waves are getting larger. As the source of the sound approaches me, the higher pitch frequency becomes a lower pitch frequency.
The issue is, however, that the light from each slit has to travel a different distance to reach the screen. When the difference between these distance is exactly N wavelength + 1/2 wavelength of the light, the two waves will destructively interfere and produce a dark spot on the screen. When the difference is a multiple of the wavelength, the two waves arrive in phase, and produce a bright spot.
When two waves which have different frequencies interfere, beats will be heard. The beats are points where the amplitude (volume in the usual case of sound) reaches a peak. The frequency of thebeats can be calculated by fbeats = f1-f2. Meaning the beat frequency will be the difference between the two frequencies.
Water : When there is something blocking waves in the water, say, a log floating in it, immediately behind the log will be calm water, but eventually the waves wrap around it. This is due to diffraction,meaning as the waves go through, the motion of the particles affect those, not just in the direction of propagation, but also to the side, allowing the wave to spread to the side as well as forward. If waves were passed through a thin slit, they would form a semi circle point source, just like light in the double slit thing.
Sound : Just like water, sound can trace around obstacles, and join back up on the other side, or pass through a thin slit and form a sort of point source. This also shows that both longitudinal and transverse waves act in the same way with respect to diffraction. 041b061a72