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Student Difficulties in Understanding Mechanical Waves:
An Overview of Previous Research Results
University of Maryland, College Park
Physics Education Research Group
22 May 1996
Outline of Questions and Concepts:
Outline of Questions and Concepts:
A. How to describe a wave
- What exactly is a wave: a propagating disturbance where the movement or forces or pressure changes at one point affect the nearest neighbors into making a similar movement, etc.
- Difficulties in representation: using 2 variables in the algebra, which coordinates are chosen for graphing, relationship between quantities, how to sketch pictures
B. How do mechanical waves interact with the medium (when created)?
- What causes the motion of the wave to change: misunderstanding the way a wave is produced and the effect this has on the propagation (and speed) of the wave?
- What properties of the medium determine the speed of the wave and the shape that the wave will have in the system?
C. How do mechanical waves interact with each other?
- Superposition of pulses or waves: how to treat the displacement from equilibrium as a vector quantity so that net displacement is the vector sum of the displacement caused by each wave.
- Interference patterns in a 2-D or 3-D situation.
D. How do waves interact with the medium when reaching a boundary?
- Describing reflection at a boundary: what physical effects are important? when does partial transmission occur?
- The phenomena leading to standing waves: understanding the superposition of reflected and incoming waves.
Introduction
The study of mechanical wave motion is important both in its own right and in the ability to use the knowledge of wave phenomena to understand more complicated phenomena, such as the wave nature of light. Black and Ogburn [1] point out that in one case, the physical results are visible as wave phenomena, in the other, the physical results exhibit wave properties and are thus the wave nature of the physical system is determined.
The most important point about student difficulties is that they all seem interconnected. When students have difficulties with separating the direction of motion of the wave from the motion of the medium, these difficulties are mirrored in the mathematical descriptions the students use. When students show misconceptions about the superposition principle, they also show misunderstanding about what a wave is. Though the following topics will be separated into different conceptual topics, the reader should keep in mind that the student conceptions are often intertwined and much less well defined than seems.
Details of the wave nature of a disturbance, wave motion, and wave interaction have been studied by few research groups. The literature is scant. The sources used in the present paper are the few published ones together the research done at the University of Maryland by the Physics Education Research Group (PERG), led by Edward F. Redish. The reader is referred to the extended bibliography for a quick overview of the papers reviewed in this paper. The reader is also reminded that not all students exhibit signs of all difficulties, and that in some cases it is impossible to hold all misconceptions at once. Statistical significance and a knowledge of how common these errors are cannot be determined. The misconceptions presented below are merely representative of common mistakes made by students.
"Correct Answer:" Important Concepts for Mechanical Waves
A mechanical wave is a physical disturbance traveling through a medium. The disturbance can involve the whole medium (as in the case of a wave on a string), only the surface layer of the medium (as in the case of a water wave), or be internal to the medium (as in the case of a sound wave). The disturbance can be finite in size (a pulse), infinite in length (a traveling sinusoidal wave, for example), or restricted to a certain volume (as a special case: standing waves). The disturbance propagates through the interaction of "nearest neighbors" in the relevant physical domain. In the case of a string, this involves tension forces (stretching) between parts of the string. In the case of a water wave, surface tension and conservation of volume play the central roles. In the case of sound waves, pressure and density play the main roles. In each case, a different physical interaction is needed to understand the propagation of the wave. Still, general ideas of wave motion and descriptions of wave properties are possible and necessary in each case.
Three general domains exist in terms of the interaction of waves with their surroundings.
- The first domain of interaction is when a wave is created in a medium as the medium is disturbed at some boundary. The disturbance must then be able to propagate through the medium. For a wave to propagate for a lengthy amount of time, the medium must have low damping and low dispersion. The speed of propagation depends on properties of the medium and not the manner in which the wave was created.
- The next domain of interaction is within the medium, when two waves meet. The principle of superposition describes the vector sum of displacement from equilibrium due to each individual wave and holds for regions where linear effects exist (in the wave equation). Large amplitude waves on strings, for example, are not linear. Superposition effects lead to interference patterns when viewed in more than one dimension.
- The third domain of wave interaction is when a wave traveling in a medium reaches a boundary to the medium. The reflection and transmission properties of waves are dependent on the properties of both the medium in which the wave is propagating and the medium that borders on it.
What is a Wave? How is it Created?
In the student's mind, what is a wave? The difficulties exhibited by students are not easily classifiable. As shown by the Physics Education Research Group at the University of Maryland (PERG), [2] students do not always consider a wave to be a traveling disturbance consisting of any displacement of the medium from equilibrium. Instead, the relevant measure of a pulse is only its amplitude (the point of maximum displacement) and the rest of the pulse is ignored. Similarly, Linder and Erickson [3] point out that "some students went so far as to claim that they felt that it was a mistake to think of sound as a wave." These students seemed to have no operational definition of a wave. If sound is not a wave, then what is it? These same students were unclear on that point.
In terms of describing a wave, students often overextend the use of sinusoidal curves both in mathematical and in graphical descriptions. Diane Grayson [4] points out that students want to draw curved lines even when parts of the waves consist of straight lines because "waves should be sinusoidal" (a student comment). The PERG [5] has shown similarly that students use (infinite) sinusoidal functions to describe localized pulses.
Furthermore, students use a different operational definition of a "wave equation" than physicists do. To a physicist, every function that satisfies the wave equation (a partial differential equation) describes a propagating wave, no matter what its shape and other properties. To a student, a "wave equation" refers to the specific equation that describes an individual wave in a single situation. [6] Thus, students often think of each wave as an individual thing, and they do not look for similarities between the phenomena common to all waves. This fragmentary approach to describing a wave is common to all topics of student understanding of waves (a topic that will be addressed more directly below).
A wave is created by disturbing a medium, after which the wave propagates through the medium. The two events are independent of each other, meaning that a change in the way the wave is created does the change the manner in which the wave propagates. Students do not separate these two events. Joseph Snir [7] points out that students have a very vague notion of what physical effects influence a wave and which parameters affect a wave. A wave contains something called strength, energy, or intensity. This students concept connects amplitude, frequency, and velocity, and any of the properties of a wave may affect the others. As an example of this, the PERG [8] has shown that students believe that a more intense or powerful creation of a wave will create a faster wave. This naive force idea shows that students revert to a vocabulary and understanding of physics similar to the one with which they entered a physics curriculum as they approach a new topic.
Both of the previously mentioned studies were done on the topic of waves on a string. Linder and Erickson [3] and Linder [9] have investigated the same question with sound waves. They have found that students have similar ideas about strength and impetus of waves. A sound wave with more impetus will travel faster (e.g. yell louder). Similarly, a wave feeling less "sound resistance" from the medium in which it travels will move faster. Also, students pointed out that speed was a function of inertia reduction; inertia was the resistance to motion in the system. Other examples of similar ideas exist. [3,9]
In general, many students seem to have only a vague idea of what a wave is. The connection between how the wave is created and how the wave propagates is also not clear to many students. The mixture of terminology used by students in their descriptions shows that they approach the subject with only a weak understanding of what their knowledge means. Results by the PERG [10] have shown that students can give contradictory descriptions of the same physical system depending on what form of question is used to trigger their understanding. When asked for a physical description of a wave, students will give an answer which may change as soon as a (misunderstood) mathematical element is introduced. This implies that students' fragmented knowledge is susceptible to different triggering mechanisms, and that the students are not seeking consistency checks between their different modes of understanding a situation. As pointed out earlier, this problem exists throughout all student understanding of mechanical waves.
Propagation of a Wave Through a Medium
After a wave has been created, the wave will move through the medium. Usually, instruction emphasizes those perfect cases where there is no dispersion and no damping within the system. Students do not so readily accept these assumptions, and insist on introducing friction and other damping mechanisms. [6] Beyond this, students have large difficulties understanding the propagation of a wave through a system.
Student difficulties with the propagation of sound waves have been extensively studied. [3,9] Students have many different mechanisms for a understanding the manner in which a sound wave travels. Both microscopic and macroscopic mechanisms are used. The microscopic mechanism involves sound as an entity carried by traveling molecules or transferred from one molecule to the next by collisions. The global properties of density and pressure are not considered. The macroscopic mechanism involves a traveling substance, such as air flowing. In both cases, students have the medium moving in order to transport a sound wave. The more molecules carry sound, for example, the more sound is carried. [9] This is related to the idea, expressed earlier, that sound is not necessarily treated as a wave phenomena. Possibly, some students think of sound as flow, such as water flow, from one place to another.
The PERG [11] has done preliminary work to show similar difficulties with respect to the difference between the motion of the wave and the motion of the medium as a wave propagates through the medium. In the context of sound, students also have difficulty distinguishing the motion of the wave from the motion of the air in which it travels.
The student difficulties with sound are illustrated in the context of waves on a string in a different fashion. Many studies [4,5,7,8] have shown that students have a difficulty separating the motion of the medium from the motion of the wave. For a longitudinal wave, the motion of the two is not always in the same direction, for a transverse wave the motion of the two is always orthogonal. Students do not always make this distinction.
Diane Grayson [4] has done extensive work on how students approach the description of waves from a kinematic point of view. Her work shows that students have difficulties gathering information from a simple graph of y vs. x, where y measures the displacement from equilibrium at a certain x, and x measures the distance down the string from a certain origin. her research includes the development of computer software to address these difficulties in the context of transverse waves. In one case, her students asked that the software include a comparison of the transverse motion of a piece of string and its motion in the direction of the wave. Thus, the students, in the correct setting recognized that they had difficulties with these concepts. Furthermore, Grayson has showed that students have difficulties applying kinematics definitions from one dimension into the context of two dimensions. For example, students take the spatial slope of the wave to find the velocity of the string at each point along the string. This confusion shows that students have difficulty using some of their algorithmic approaches to understanding when these algorithms are placed in a new setting. Taking the slope with respect to time (at each spatial point) and not with respect to the spatial variable would give the correct answer for the velocity.
Results at the University of Maryland supports this result in different types investigations. As mentioned earlier, [8] students confuse the ability of a change in the initial transverse motion that creates a wave to change the speed of propagation of the wave. These same students, in interviews, often mistake the manner in which a wave propagates, and have difficulty separating the motion of the medium from the motion of the wave. This result is corroborated by the fact that students also confuse these two motions when describing them mathematically. [5] In the case of a pulse traveling along a string, using the same coordinates as described before, students often confuse the variables x and y. They do not operationally distinguish between the two. Thus, they make the mathematical mistake that others have found in student conceptual understanding. Sometimes, the variable x is defined as the distance that a pulse has traveled down the string. In this case, students confuse propagation with the description of the string itself.
Interaction of Waves with Each Other
When more than one wave propagates through a medium, the waves at some point may interact. Examples of this are water waves overlapping, waves on a string traveling in opposite directions, or sound wave interference from two loudspeakers. Students exhibit strong beliefs about the manner in which waves combine. Preliminary results [7] showed that many students believe that waves on a string cancel when they meet. Further results [2] show that students answer this way only in special cases, and student responses are far more varied.
Students treat constructive and destructive superposition differently. Though using similar language, they use different reasoning to describe the behavior of the strings and the waves as the pass by each other for each case. In the case of two symmetric pulses with equal displacements in opposite directions, waves cancel at the moment of maximum overlap. Students often draw complete cancellation even for other moments. For asymmetric waves or waves where the amplitudes are not the same, students often inappropriately cancel waves completely. Thus, cancellation is an constant property of destructive superposition. For people who make this mistake, vector displacement due to each pulse is not added. Instead, "waves cancel" is given as a reason for the shape of the string. No operational definition beyond cancellation exists.
A similar phenomenon exists in the case of constructive interference, but rather than overextending the applicability of a special case, now students restrict the use of the common model. Many students use the phrase "waves add" without defining the mechanism with which they add. The most common error students have is only adding pulses when they are at maximum overlap. They don't treat superposition as a point by point addition of displacement. Instead, only when "the amplitudes overlap" (meaning, the highest point in the pulse, according to a student comment) is there any addition. Otherwise, the point of highest displacement due to one or the other pulse is chosen as the displacement of the string.
A common error found in constructive superposition is that students make an analogy between pulses and particles traveling toward each other. Equal size pulses will bounce off each other. Large pulses will cancel out smaller ones, and then keep going in their original direction (though smaller by the amount canceled out by the smaller pulse). In both cases, the students treat the wave as a carrier of energy or momentum (or strength or impetus), and interaction of waves is like a collision between particles. The size afterward seems indicative of less energy in the wave. Here, again, the vague terminology and incorrect interpretation of representations, together with the mixture of interchangeable concepts shows that students have only a vague understanding of the situation and are reaching for other ideas and concepts to describe things that do not make sense to them.
Difficulties with superposition in more than one dimension have been seen6 but not investigated in detail. The results from one dimension seem translatable to further dimensions. Students have difficulty understanding different representations, and the question of "what adds" still arises. The topic of superposition in more than one dimension, usually referred to as interference, plays a large role in the study of the wave nature of light, so it is important for the student to have a firm knowledge of the phenomena of superposition with mechanical waves. This seems not to be the case.
Brief Overview of Other Misconceptions
The previous discussion has emphasized ideas that are quickly taught in most university settings. Students are exposed to far more material than this. Most instruction in waves deals with standing waves. But, to understand how a standing wave can be created, students must understand the idea of reflection. Neither of these two topics has been investigated in great detail. [6,12]
Students often have waves or pulses incident on a boundary simply disappear. The substance on which they are incident absorbs the waves completely. If a wave or pulse is the reflected, it comes from inside the wall, also. In the case of a pulse traveling down a string, students also have difficulty knowing if the pulse is reflected on the same side or opposite side, depending on the special cases of free or fixed boundaries. In the case of semi-free or semi-fixed boundaries (between one type of string and another with greater mass density, for example), students have no clear idea or conception with which to approach the problem. Most seem not to recognize that there should be reflection in such a case.
Standing waves are the superposition of reflected waves and incoming waves under the appropriate boundary conditions. Most students take standing waves on a simple phenomenological ground, and textbooks [13] also usually do not explain in detail how standing waves come to be. The description of standing waves can be taught at this level, but most wave phenomena are no included in instruction in this case. When asked, [6] most students seem unaware of the connection between standing waves and the phenomena of superposition, reflection, wave propagation, and boundary conditions. Again, this shows evidence that students do not have an integrated understanding of wave phenomena, and are unable to apply their fragmented knowledge to situations outside of the ones used to teach them.
Conclusion
In general, all of these studies show that students are taught certain terms, but they are unable to distinguish between the concepts involved in each term. Teaching only the vocabulary, only the graphical description, only the mathematics, or only the conceptual meaning of a thing is not effective. For students to show true understanding of mechanical waves, they must be able to distinguish between concepts, and describe the differences in many different ways. To have an integrated understanding of mechanical waves, students must be able to differentiate between concepts, be able to apply these concepts, and be able to describe them. If students are not aided in this process of combining understanding and representation, they will have a much harder time using their knowledge and being aware that their knowledge is correct.
End Notes
1. Black, P. J. and Jon Ogburn, "Which Waves?"
Physics Teaching, GIREP. U. Ganiel, Editor, p. 421 - 433 (1980). (link to summary)
2. Wittmann, Michael C., Edward F. Redish, and Richard
N. Steinberg, "Identifying and Addressing Student Difficulties with Mechanical
Waves," SEPA/MD/Del regional AAPT conference, York, PA, 2 Mar. 96. (superposition).
(link to summary)
3. Linder, Cedric J. and Gaalen L. Erickson, "A
study of tertiary physics students conceptualizations of sound," Int. J.
Sci. Educ., 11 (1989) 491 - 501. (link to summary)
4. Grayson, Diane, J., "Using Education Research
to Develop Waves Courseware," Computers in Physics, 10:1 (1996) 30 - 37.
(link to summary)
5. Steinberg, Richard N., Jeffery M. Saul, Michael C.
Wittmann, and Edward Redish, "Student Difficulties Understanding the Told
of Mathematics in Introductory Physics," Bulletin of the American Physical
Society, 41:2 (1996) 869. (link to summary)
6. Physics Education Research Group, University of Maryland,
general comments in research notebooks, private conversations, and individual
interviews (1995 - 96).
7. Snir, Joseph, "Making waves: A Simulation and
Modeling Computer-Tool for Studying Wave Phenomena," Journal of Computers
in Mathematics and Science Teaching, Summer 1989, 48 - 53. (link to summary)
8. Wittmann, Michael C., Edward F. Redish, and Richard
N. Steinberg, "Identifying and Addressing Student Difficulties with the
Speed of Mechanical Waves," American Association of Physics Teachers, to
be presented at College Park, August 1996. (link to summary)
9. Linder, Cedric J., "University physics students
conceptualizations of factors affecting the speed of sound propagation,"
Int. J. Sci. Educ., 15:6 (1993) 655 - 662. (link to summary)
10. Saul, Jeffery M., Michael C. Wittmann, Richard N.
Steinberg, and Edward F. Redish, "Student difficulties with math in physics:
Why can't students apply what they learn in math class?" American Association
of Physics Teachers, to be presented at College Park, August 1996. (link to
summary)
11. Wittmann, Michael C., Edward F. Redish, and PERG,
"Student difficulties with the wave nature of sound," unpublished
analysis of results, 1996.
12. Wittmann, Michael C., Edward F. Redish, and PERG,
"student difficulties with reflection from a boundary," unpublished
analysis of results, 1995.
13. See, for example, most common textbooks for the
introductory level, e.g. Tipler, Halliday and Resnick, Serway, etc.
Papers not cited:
Paper by Snir and Livna, referred to as being "in press" at time
of cited paper.
Linder's thesis on the subject of student conceptualization of sound.
Grayson's thesis, which was read but not cited since all ideas were in cited
paper.
Richard N. Steinberg's paper on physical optics (in press), given as a talk
in Orlando, January 1995, while part of the Physics Education Group at the University
of Washington, Seattle.
Bibliography:
Summary Notes on Papers: (alphabetical)
Black, P. J. and Jon Ogburn, "Which Waves?" Physics Teaching, GIREP. U. Ganiel, Editor, p. 421 - 433 (1980).
- Reasons for doing water waves, and the mechanics of making them, the physics of understanding them, a long introduction on the conceptual necessity of waves (this introduction was the most useful part of the paper). Noteworthy concepts:
- Wave motion is independent of medium motion in both speed and direction (sometimes).
- There are many different types of propagating disturbances, from finite to infinite in length, and with many shapes. The general idea of propagating disturbance should be emphasized the most, and generalized away from the popular conception of a "wave."
- There are different amounts of medium interaction: total (rope), surface (water), internal (sound).
- Don't use "artificial waves," try to relate to actual experience of the student.
- Speed depends on the medium, therefore some emphasis should be placed on the dynamics of this and not just the kinematics/formulas.
- Emphasize superposition.
- Results should be generalizable to invisible waves: in once case, one sees the phenomena and says that all waves behave this way, in the other case, one sees the phenomena due to "invisible" causes and say this must be a wave.
- Stay away from standing waves being introduced too soon, and don't confuse waves with other waves (e.g. vibrating string = standing wave creating sound wave...)
- Waves to study should: be visible, relevant, real, and linear, and have low damping and dispersion.
- Methods: none, since it is not a research paper, but a paper outlining phenomena to be emphasized in an understanding of waves.
Grayson, Diane, J., "Using Education Research to Develop Waves Courseware," Computers in Physics, 10:1 (1996) 30 - 37.
- Paper focuses on applying kinematics to waves immediately after learning kinematics in one dimension: given y vs. x, graph y vs. t and x vs. t for a point, and v vs. x for the string.
- Difficulty in separating the motion in one direction from the motion in another when dealing with transverse waves (introduction of discussion of two different directions of motion had marked effect on understanding in study population).
- Attempt to get v vs. x graph from taking slope of y vs. x graph: misapplication of an algorithm from kinematics.
- Desire to draw curved lines (comment: "I'm just used to drawing sine curves...").
- Difficulty in distinguishing between a picture or a pulse and the graph of y vs. x for the pulse. Could be the same shape on the page, but one has coordinates. Study population suggested separating these two things.
- Methods: interviews with students, observation of students using computer programs (usability testing)
Linder, Cedric J., "University physics students conceptualizations of factors affecting the speed of sound propagation," Int. J. Sci. Educ., 15:6 (1993) 655 - 662.
- Analysis of conceptions used by students to look at sound, not necessarily about its wave nature.
- Speed of sound determined by physical obstruction caused by molecules in medium (related to naive force idea in PERG work, in the sense of friction, which he calls "sound resistance.")
- Speed of sound is a function of molecular separation.
- Speed is a function of inertia reduction, so if you reduce the inertia, it will change the speed of sound.
- More molecules carry more sound (together with sound as traveling energy, the idea can almost be interpreted as thicker tube = more flow, or mass transports better)
- Speed of sound depends on compressibility of medium (similar to #2 but this time in a macroscopic description, it seems).
- Common factor he points out: students are taught certain terms but they invent the definitions of these terms and the physical meaning of these terms on their own.
- Methods: phenomenographic study, interviews analyzed in great detail to uncover conceptions held by students.
Linder, Cedric J. and Gaalen L. Erickson, "A study of tertiary physics students conceptualizations of sound," Int. J. Sci. Educ., 11 (1989) 491 - 501.
- Analysis of conceptions used by students to look at sound, not necessarily about its wave nature.
- A microscopic perspective described by the students:
- sound is an entity carried by individual molecules through a medium (in terms of wave, transport of the medium with the wave)
- sound is an entity that is transferred from one molecule to another through a medium (in terms of waves, a medium which is loosely bound, like a chain of balls attached by rubber rods, transporting a wave without understanding how the wave and the medium interact).
- A macroscopic perspective:
- sound is a traveling bounded substance with impetus, usually in the form of flowing air (again, transport of the medium to create the wave, but with the naive force idea playing a role)
- sound as abounded substance in the form of some traveling pattern (a traveling disturbance, where the disturbance and the wave are independent of each other; possibly means students have different operational definitions for the two)
- Difficulty in matching sound phenomena to wave concepts as described in "a mathematically abstract modeling system." Wave conceptualization divorced from conceptualization of sound, and "some students went so far as to claim that they felt that it was a mistake to think of sound as a wave."
- Methods: phenomenographic study, interviews analyzed in great detail to uncover conceptions held by students.
Saul, Jeffery M., Michael C. Wittmann, Richard N. Steinberg, and Edward F. Redish, "Student difficulties with math in physics: Why can't students apply what they learn in math class?" American Association of Physics Teachers, to be presented at College Park, August 1996.
- Problems students have with knowing how to approach a topic, calling on the wrong information at the wrong time.
- When given a mathematical representation of whose interpretation they are unclear, students will use their interpretation of the math to describe the physical situation.
- But, the interpretation of the physical situation does not necessarily depend on the order of presentation (first physics, then math, vs. first math, then physics). Some students will revise their answer for the physical situation to match their mathematical description.
- Methods: analysis of free response conceptual questions, interviews pre and post instruction (though pre-instruction interviews not conclusive).
Snir, Joseph, "Making waves: A Simulation and Modeling Computer-Tool for Studying Wave Phenomena," Journal of Computers in Mathematics and Science Teaching, Summer 1989, 48 - 53.
- Not necessarily a research paper, though it refers to a paper by Snir with J. Livna, "Students Conception of Waves," which was in press at time of this paper.
- Frequency is analogous to time, not 1/time. Phase and phase velocity are also difficult concepts for traveling (sinusoidal) waves.
- Inability to distinguish between motion of the medium and the motion of the wave/pulse.
- The wave has some sort of "strength" or "energy" or "intensity:" something that is essentially a mixture of amplitude, frequency, and velocity. Any of theses interchangeably affects the other (related to work done by PERG, see Wittmann).
- For superposition, many students have the waves cancel out.
- Methods: interviews of students.
Steinberg, Richard N., Jeffery M. Saul, Michael C. Wittmann, and Edward Redish, "Student Difficulties Understanding the Told of Mathematics in Introductory Physics," Bulletin of the American Physical Society, 41:2 (1996) 869.
- Mathematical problems analyzed, little focus on conceptual work, but a few things stand out:
- Confusion between spatial and temporal dependence implies that students have a hard time combining an understanding of each of the two (this is born out in other PERG research, see Wittmann).
- A wave should be sinusoidal, and not a pulse, viz. students have desire to not just write a sinusoidal equation for a pulse, but call it the wave equation also.
- Confusion about propagation and transverse motion of an element of the system, as evidenced through the mathematical description which confuses the meaning of x (is it the distance that the wave has propagated or the free variable describing position along the string?).
- General points: students have difficulty with representation (failure to recognize the relationship between physical situation and mathematical formalism), with coordinatization (inability to tie different representations to a well defined coordinate system), with functions (inability to understand and apply the idea of a function).
- Methods: analysis of examination questions, free response conceptual quizzes, and individual demonstration interviews.
Wittmann, Michael C., Edward F. Redish, and Richard N. Steinberg, "Identifying and Addressing Student Difficulties with Mechanical Waves," SEPA/MD/Del regional AAPT conference, York, PA, 2 Mar. 96. (superposition)
(link to slide presentation as presented in York)
- Problems with superposition analyzed in detail, mostly dealing with constructive superposition, though data exists also for destructive superposition.
- Students treat constructive and destructive superposition differently, applying different concepts to each phenomena (from fall 95, pre-instruction data).
- Constructive superposition exists only when the peaks ("the amplitude") overlap, not as addition of displacement. Students globalize the pulse into one unit, like a particle, and choose one relevant measure to determine interactions.
- The energy model: superposition as either an elastic collision (pulses bounce) or an inelastic collision (larger pulse cancels out smaller pulse, where size is a measure of strength, again the naive force idea).
- Methods: analysis of free response conceptual quizzes, specially designed diagnostic test, and individual demonstration interviews, both pre and post instruction.
Wittmann, Michael C., Edward F. Redish, and Richard N. Steinberg, "Identifying and Addressing Student Difficulties with the Speed of Mechanical Waves," American Association of Physics Teachers, to be presented at College Park, August 1996.
- Problems students have with determining what affects the speed of a wave.
- The naive force idea: students are unsure of what has to be done, but force or energy play dominant roles. Students revert to a anon-physics definition of both terms, evidenced in terms such as "harder" and "more strength."
- Inability to distinguish between motion in one direction (transverse to direction of propagation) and motion in another (propagation). This refers especially to the idea that a faster transverse motion will cause a faster pulse propagation.
- Methods: analysis of free response conceptual quizzes, specially designed diagnostic test, and individual demonstration interviews, both pre and post instruction.
Michael Wittmann
Department of Physics and Astronomy
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