Motivation for unit

A substantial challenge facing high school science teachers is the task of making general science curricula relevant and accessible to students without making it trivial. Fun demonstrations and activities sometimes replace legitimate objectives and quality science in the interest of temporarily snagging student interest. While this approach no doubt makes science seem “cool”, it fails to portray an accurate view of science or convey useful skills and knowledge. The challenge, therefore, is to maintain student interest without abandoning the high level content. This unit seeks to do this with the topic of waves by centering the unit on a topic of common student interest, music, and using that to guide the study. In this way, the unit will simultaneously achieve the goal of attracting student interest and maintaining rigor in the content studied.

The general theme and structure for this unit will be using what is known and familiar, both in terms of scientific content and the context of the unit, music. Students tend to have much more success and are willing to take greater risks when they feel some level of comfort and independence in the subject area. This comfort is facilitated by grounding the unit in what is known. However, despite the theories that we increasingly need to teach to the “hip-hop generation” and incorporate students’ funds of knowledge (Moll, 1992), framing new knowledge entirely in the context of what is already known prohibits students from opportunities to expand their knowledge and extend the boundaries of their academic comfort. Thus while students may feel comfortable with a specific genre of music, namely hip-hop, many are largely unfamiliar with other genres. In order to facilitate several aspects of music and the application of the principles of waves, students will encounter a number of genres and characteristic musical instruments during the course of the unit.

Student background knowledge

The physical science curriculum begins with an introduction to basic units of measurements, including length and time. Students encounter these units in the context of measuring physical objects, and apply them to the concepts of speed, velocity, and acceleration in the early units of physics in the physical science curriculum. In the context of this unit on waves, which puts so much emphasis on sound and light waves which have visible effects but whose actual physical parameters, such as wavelength and speed, are not visible, it is critical to base a discussion of these properties for waves on a physical understanding. The most important parameters for the study of waves are length, time, and speed. Students will also be introduced to the concept of frequency, which will be a new topic to the students at this point.

Wave basics

Fundamental to the definition of waves as a disturbance that propagates through a medium, transmitting energy, are the concepts of energy and the idea of a disturbance moving rather than the entire medium. The majority of topics encountered in physical

science and other early science curricula deal with concrete objects—balls, cars, and such—moving in observable ways, such that the idea of a wave presents a new and different phenomenon. As a result, dealing with student misconceptions about the structure and nature of the waves up front is critical. A wave differs from a classical particle, such as a ball, in that it is not a single “object” moving through space. Rather, it is a change, either transverse or longitudinal, in the arrangement or position of parts of a substance. The exact nature of this change depends on the type of wave and the medium.

One way to bridge the gap between an understanding of the motion of particles and the motion of waves is to consider a slinky or other spring-like tool. Unless you plan to throw the slinky across the room, in which case it will behave like a particle, the slinky can be used to demonstrate wave motion in a medium that is visible to students, with equally visible consequences. A general problem I have encountered when trying to convey abstract concepts is that without some means of visualizing it, the students are not able to manipulate the idea to meet new and different situations and the topic remains abstract and paper based. At the same time, a too-pervasive analogy likewise restricts students’ abilities to expand past the suggested example. Therefore, the introduction of the nature of waves must be structured in such a way that students grasp the concept that a wave is a moving disturbance without being restricted to the examples of a slinky or telephone cord. Otherwise, students will not grasp the connection between a graph drawn on a board and light and sound waves. This can be done by taking a two-pronged approach: observing the position of an entire medium at a single point in time, and observing the motion of a single point throughout time.

Once the nature of wave as a disturbance has been established, it is a fairly straightforward jump to explaining how waves transfer energy, particularly how this varies from a particle, and a graphical 2D representation of a wave. By this point in the year, students should be familiar with the ideas of energy and force, with a particularly heavy emphasis on potential and kinetic energy. While “light energy” is previously discussed briefly to the extent that it exists in light sources, there is no mention of how this light energy varies between types of light and why, and therefore up to this point is a simple matter of identification. Understanding that waves transfer energy and then identifying light as a wave would enable students to make better sense of the term “light energy”. In order to do this, physical demonstrations and observations of propagating waves serve as a useful tool: students can observe that in a mass oscillating on a spring energy is being transferred from potential to kinetic and back again, and that each kind of energy is being transmitted through the medium, eventually reaching the other “end.” The challenge remains to demonstrate that rather than the entire physical object moving through space, a disturbance is propagating within a given medium, but this can be done with the aid of graphs.

The target audience for this curriculum is students who are concurrently taking Algebra I, and are therefore not familiar with periodic functions such as sine and cosine.

As a result, the representation of a periodic event in graphical form will be a new concept. Waves are typically graphed as functions of time, in which the motion of a single point is referenced, and the properties of wavelength and amplitude are defined in reference to this graph. If students have developed a familiarity with physical waves, the transition from looking at many points moving in a physical object to the description of a single point as time continues could be confusing. However, graphs of wave are particularly useful for defining and representing various wave properties, and the ability to interpret and explain graphs is a fundamental skill for students studying science, as it develops analytical skills and reinforces the aspects of science requiring creating models of situations. Such abstract concepts force students to operate on a much higher level than typically expected. One approach for tying the graph to the motion of a single point is to have students exclusively observe a single point, and describe the motion of that point, rather than focusing on the motion of the entire medium, which is particularly tempting when using such items as a slinky or telephone cord. The shape formed by the whole medium very closely resembles the graph of the position of a point in time. Because each can be used to obtain different information (for example, the period of the wave as compared to the wavelength), the two must be distinguished. With both representations, students will be able to describe all of the fundamental features of the wave.

At this level of science, students should be familiar with the concepts of wavelength, frequency, speed, period, and amplitude. An understanding of each of these is necessary for students to describe the way waves interact to generate the sounds heard in music, and how changing each of these factors might change the resulting sound.

Wavelength is perhaps best described as the distance between one peak disturbance and the next. This description is useful whether one is talking about water waves, slinky waves, or sound and light waves. It can also be easily located on a diagram of a wave. The frequency, or number of wavelengths to pass a point in a given amount of time, can be a confusing concept if introduced solely mathematically. However, using physical demonstrations (and prior familiarity with other concepts such as current in which the number of things to pass a point in a unit of time is used to define the concept), it is fairly straightforward to show that if you stand at a particular place, a series of peaks passes by you. The greater the speed of the wave (another familiar concept), the more often a peak disturbance passes by, and the less time passes between subsequent peaks. With this single demonstration, we can therefore introduce speed, frequency, and period, all interrelated concepts, without relying too heavily on an immediate interpretation of a mathematical description. This will in fact make the mathematical description much more accessible to students.

Sound and Waves

A major feature that is lacking from the Physical Science curriculum as structured in the Philadelphia Core Curriculum is an overall coherence between the units taught.

Students are briefly introduced to Chemistry, Physics, Earth Science, Space Science, and

Environmental Science, and the largely factual approach often minimizes the connection between subsequent units. This unit therefore presents an excellent opportunity to incorporate some of the prior topics, such as motion, force, and energy. The motion is easily incorporated into the discussion of wavelength, frequency, and speed, using the concepts of displacement and velocity. Force and energy can be fairly easily incorporated into the discussion of physical and visible waves, such as in a slinky, because students can see and feel the work required to generate the wave. This connection becomes somewhat less easy to grasp with sound and light waves where the source of the wave energy is not as specific, and factors leading to wave dissipation are not as obvious.

However, this is another situation in which thorough familiarity with a wave in one context will make extensions to another more complex and abstract context more manageable. Students will thus be able to deal with the concept of wave dissipation as a manifestation of energy transfer and connect the volume of sound to the amount of energy present in a sound wave. While this may seem to be something of a stretch for a basic Physical Science course, tying various topics together as well as explaining observed phenomena is critical to making the course meaningful and worthwhile.

Another challenging but essential concept for students is the difference between a transverse and longitudinal wave. Visualizing the application of wave characteristics such as the crest, trough, and wavelength are fairly simple with a transverse wave. In a compression, or longitudinal, wave, the disturbance in the medium no longer takes the shape of what we typically imagine as a wave. However, the same principals apply: rather than talking about a crest, we talk about a compression which is a region in which the medium has maximum density due to the disturbance. Replacing a trough is a rarefaction, where the medium has a minimum density. In order to tie this concept to the more easily grasped longitudinal wave, students could help to generate another graph demonstrating both the density of the whole medium with position (as in with a slinky), as well as the changes in density at a single point with time. For this type of wave, it is necessary to expand the definition of wavelength from simply the distance between two crests to the distance between any two corresponding points in a wave (two compressions, two rarefactions, etc).

Sound in Musical Instruments

Ideally, the emphasis in my classroom is the application of the topics to an actual situation of interest. In order to do this, students must be able to see how the properties of something govern its behavior. Waves are a particularly suitable topic for this approach as a number of fascinating phenomena with which the students are founded on the properties of waves. While most students do not have a great deal of experience with instrumental music, some participate in the school band, participate in a choir, or have some other meaningful relationship with music. We will therefore use musical instruments as a vehicle to discuss wave properties in general, and later in the unit as the primary means for introducing sound-specific topics.

Among the musical instruments involved in jazz are brass instruments, such as the trumpet and trombone, stringed instruments such as the bass and occasionally violin, and percussion instruments such as the piano and drums. Each of these demonstrates particular features of sound and waves. This serves not only to augment the student understanding of general wave types, both longitudinal and transverse, and wave properties, such as frequency, wavelength, and amplitude, but also to introduce the

music-specific concepts of resonance and pitch. First among these phenomena is how the structure of the sound wave relates to what we observe: the pitch of a sound is determined by its frequency: higher pitch leads to higher frequency; the volume of the sound is determined by the amplitude of the wave, and the amplitude does not affect the pitch.

Musical instruments produce various forms of standing waves in order to create the complex sounds we hear. While the complete waveform produce by a musical instrument is very complex, the basic mechanics involve a standing wave, either compressional (in an air column) or transverse (on a string) that vibrates at different frequencies, as determined by the length either of the air column or the string, to produce a specific sound. A standing wave is created when the frequency of the wave in the medium causes reflected waves to interfere with source waves so that parts of the medium (called nodes) appear to be standing still. Different musical instruments produce different types of standing waves, but each instrument has a set of natural frequencies corresponding to its size and shape (length); each of these natural frequencies corresponds to a certain formation of standing waves in the medium. The complexity of sound waves lies in the fact that for a particular length of the medium (air or string), several standing waves can be produced, known as the first harmonic (or fundamental), second harmonic, etc. These are particularly easy to visualize for stringed instruments because the formation of the waves lines up with our basic understanding of waveforms. (The Physics Classroom, 2004)

Stringed instruments, both pianos and the violin family, rely on strings to produce the initial vibrations. In order to produce the actual sound that reaches our ears, both types of instruments require an additional resonator (essentially a shaped box) to produce vibrations with sufficient magnitude that the sound reaches our ear. This is because the size of vibration in the air produced by the string alone is too small to create a discernible sound. While the violin follows the pattern of first, second, and third harmonics in exact whole number multiples of the fundamental frequency fairly well, the piano departs from this increasingly as the frequency increases. However, the approximate understanding is sufficient for this introduction to musical instruments and sound principles. Both types of instruments rely on strings under tension; when these strings are pulled from their rest position, they vibrate at the natural frequencies described above. The strings are attached to the resonating box which in turn produces the vibration that reaches our ear. In a piano, when a key is pressed a hammer covered in felt hits the string of the appropriate length.

In a violin, the string can either be plucked or bowed. The shape of the instrument as well as the method of producing the sound change the timbre, or sound quality. A hammer with the wrong felt quality will produce a sound that is either too harsh or too mellow; a violin bow with too much rosin will produce a scratchy sound. While this interferes with the quality of the sound and some of the more enjoyable complexities of the sound, the basic vibrational pattern of standing waves remains the same. These instruments can be artificially simulated in a classroom using strings stretched across a box. (Hutchins, 1948)

Woodwinds and brass employ different systems of creating the sound and therefore have different sound qualities; however, they both rely on changing the length of a vibrating air column to create different sounds. Woodwind instruments use a reed (either single or double) which creates the vibration in the air column by converting a steady stream of air into a series of puffs, creating the compressional wave that is the basis of wind instruments. The exception to this is the flute, which functions like an empty soda bottle in that the vibrations are produced when air is blown across an opening; for the reed based instruments, the puffs come when the reed is opened, and stop when the reed is shut. These two different systems of sound production lead to two different patterns of standing waves, depending on the end condition required. In order to change the wavelength, the wind instruments rely on a set of keys or openings in the bore: if these openings are sufficiently large, the location of the opening essentially determines the wavelength and therefore the natural frequency of the instrument. Most wind instruments rely on a set keys to produce whole tones, and various combinations to produce intermediate tones. Higher pitches of the same “note” (A, B, C, etc) can be produced either with special keys or by blowing harder.

Brass instruments likewise create varying pitches by changing the length of the air column: trombones by changing the position of the bell and trumpets and French horns by changing the path of the air within the column. Although the actual instrument is flared at both ends, which is largely responsible for the quality of the sound produced, a basic cylinder provides a good starting point. For the brass instruments, rather than a vibrating reed producing the vibrations in the air column as with the woodwinds, the player’s lips produce the vibrations. The formation of the lips is responsible for some of the changes in sound we hear.

By extending the study of waves to concrete objects, musical instruments, students will be able to grasp both the abstract and concrete features of waves.