PHYS 123 - General Engineering Physics III

6 CR

Third in a three-course survey of physics for science and engineering majors. Course presents fundamental principles of oscillating systems and wave phenomena, including optics, simple harmonic motion, waves, sound, light, optical instruments, interference, diffraction, and polarization. Conceptual development and problem solving have equal emphasis. Laboratory work presents methods of experimental analysis (modeling, errors, graphical analysis, etc.) and prepares students for upper-division research.

Prerequisite(s): PHYS 122.

Course Outcomes
Laboratory Skills • Use standard laboratory instruments appropriately, based on a sufficient understanding of their function; • Measure physical quantities in the laboratory with appropriate attention to minimizing possible sources of random and systematic error; • Make reasonable estimates of the uncertainties associated with each measurement; • Evaluate a hypothesis in terms of its testability and determine the kind and amount of data required to test it; • Summarize the properties of a set of data to facilitate analysis, using standard statistics such as mean and standard deviation; • Determine the uncertainty of a computed quantity that arises from the uncertainties in the measured values of the quantities from which it is computed; • Analyze an appropriate set of measurements for consistency with a hypothesis, form and justify a conclusion regarding the fit between the data and the hypothesis; • Recognizes that measurement uncertainty is estimated as an act judgment on the part of the observer and that judgment does not imply arbitrariness. Communication Skills • Produce a compact and unambiguous verbal description of an experimental procedure and of the observations/data obtained using it; • Produce a compact and unambiguous verbal description of a chain of theoretical or experimental reasoning, including clarity regarding assumptions, accuracy regarding logical connections, specificity regarding conclusions, and clarity regarding the scope (and limitations) of applicability. Physical Problem Solving Skills • Habitually sketches the configuration of problem elements as part of the problem solving process; • Habitually uses a variety of representations in the problem solving process; • Consciously selects an appropriate coordinate system; • Identifies sub-problems and breaks a large problem into parts (linking variables). • Habitually develops and interprets algebraic representations before substituting particular numerical values; • Makes appropriate use of significant figures and units in problem solving; • Interprets algebraic and numerical results in words; Oscillation Concepts Context for the objectives • Oscillating systems are characterized by a restoring force or potential and a characteristic variable whose value at a given time can be used to determine all other system variables. The dynamics of such a system is described by a unique equation that relates the restoring force or potential to the value of the parameter and its derivatives. • In a harmonic system, this relation is a direct proportion between the parameter and its second time derivative. The solution to this equation is sinusoidal in time. • The effect of the environment (if the force or potential is taken to be within the system) is restricted to setting the initial conditions for oscillation. Oscillation objectives • The student can generate the appropriate dynamics equation for simple LC circuits, for the mass spring system, and for other simple mechanical systems, through application of energy conservation, Newton’s Laws, or Kirchoff’s laws (for circuits). • The student can identify the parameters in the dynamics equation that determine the natural frequency of oscillation for the system. • The student can solve the Dynamics equation by direct substitution and confirm that a sinusoidal oscillation of the characteristic variable is a solution. • Given appropriate initial conditions the student can write a specific function for the characteristic variable and evaluate all the terms in this function. • The student understands the relationships between all of the common system variables, and the characteristic variable, and can use these relationships to solve standard end-of-chapter problems involving these variables • The student recognizes the relationship between Circular Motion and Simple Harmonic Motion and can solve end-of-chapter problems that rely on this relationship • The student recognizes the phase relationships between and among appropriate system variables and the characteristic variable and can identify or predict these relationships in questions or problems. Damped and Driven System Objectives • The student can recognize certain functions for the characteristic variable as being solutions to either the damped or driven system problem. • The student can distinguish the solutions above from each other and from the pure harmonic case, and solve end-of-chapter problems using these equations. • The student can describe the qualitative effect that the damping or driving terms have on the system. • In particular the student can describe the phenomena of resonance and can compute the conditions that will produce this phenomena. Spring Mass System Particular Objectives • The student can use the solution of the SHM problem as an input to typical mechanics problems of the type practiced in P121. LC Circuit Particular Objectives • The student can describe the energy oscillations of the system and the fields that are source of the stored energy. • The student can produce a phasor diagram for the series LRC circuit and use it to solve end-of-chapter problems. Wave Concepts Context for the objectives • One useful way to organize our thinking about wave phenomena, is to recognize that, in the first place, there is a physical system that is capable of supporting a traveling wave. Some of the properties of waves derive from the properties of this physical system. Therefore these properties will hold for all waves that propagate in that system. Then, there is the particular instance of a wave that passes in front of us. This wave was created by a source, has a particular history, and is typically confined by boundaries. Many of the properties of waves we are familiar with are determined by these transient or particular conditions that derive from the environment. Thus these properties may or may not hold from one example of a wave to the next. In the outline that follows then, we distinguish properties that derive from the system (medium), and properties that derive from the boundary conditions (including source). • As with Oscillating systems we can describe the wave in terms of a single characteristic variable. A dynamics analysis of the system produces a unique equation relating the characteristic variable to its time and position derivatives. This result is called the wave equation. The solution to this equation specifies the value of the characteristic variable as a function of position and time, f(x-ct), and this wave function describes the particular wave we observe. • Finally most of our study is focused on Sinusoidal traveling waves, and there are particular relationships that derive from that functional form. Wave objectives • Students will be familiar with the wave equation for Electromagnetic Waves and for waves propagating on a string. They will be able to identify the terms in these equations that determine the wave speed. • Students will be able to identify the following properties as deriving from the system and describe their manner of origin from the system parameters. • The physical quantity described by the characteristic variable • The Wave Speed c. • The dispersion relation lf = c • Transverse vs. longitudinal waves • The property of superposition. • Transverse vs. longitudinal waves • The expression for power or intensity of the wave. • The expression for momentum of the wave. • The orientation of E and B for E/M waves. • Students will be able to identify the following properties as deriving from the Environment. • The source determines: • Shape-f(x-ct). (pulse, train, harmonic, other) • Amplitude. • Frequency (system picks l). • Wavelength (system picks frequency). • Direction of travel. • Phase. • Transverse vs. Longitudinal if both are supported by the medium. • The boundary imposes conditions on f(x-ct) at the boundary: • Closed, Clamped, or fixed boundary, f(x-ct) = 0 at the boundary. • Open, Unclamped, or free boundary, f(x-ct) = max. at the boundary. • Note other boundary conditions exist. • Boundaries can change the direction of travel. • Boundary Conditions determine the fraction of the wave reflected. • Boundary location determines the Phase at the boundary. • Boundary Conditions determine the Phase upon reflection. • The location of other sources or reflections determines interference. • Destructive: The path difference is (m+1/2)l. • Constructive: The path difference is ml. • Other: The amplitude is determined by Df. • Standing Waves are an interference phenomena that depends on the boundary conditions. • Open/open or closed/closed L= (N/2)l. • Open/closed or closed/open L= (2N-1)l/4. • With l chosen, there is no choice for frequency f. • Students will be able to contrast and compare waves produced in common systems (light, sound, string waves, water waves) and describe their physical differences in terms of the properties noted above. • Students will be able to use a sinusoidal wave function to determine the value of the characteristic variable at any position at any time. • Students will know the meaning of all the variables used in the common forms of a sinusoidal wave function and be able to evaluate these variables from an appropriate verbal description of the wave. • Students will be able to compare the phase of two waves and determine the result of superposing these waves. Geometric Optics Concepts Context for the objectives • Geometric optics is a physical model of nature as opposed to a theory about light. As such it is a simplification of nature to a small set of principles and consequently it has a restricted range of applicability. Since this restricted range nevertheless encompasses most of ordinary experience, it is a powerful and useful model. Geometric Optics objectives • Students will understand that Geometric Optics is a physical model and be able to identify the conditions that govern its applicability. • Students will be able to describe the principle statements that comprise the model. Elements of the Model • Light travels in straight lines. This motion has direction. • Light can pass through other light without distorting either beam. • The path of light can be blocked by an object • Light is emitted in all directions by every point on an object. • From the point of view of optics an object is a collection of points from which many light rays diverge. • Some objects generate the light on their own (sources). • Other objects are only visible when the light from sources falls on them. • We see light when it enters our eye, and the eye must be directed back along the direction of the incoming ray. Looking, is a

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