Gravitational-wave Science in the High School Classroom
aa r X i v : . [ phy s i c s . e d - ph ] A ug Gravitational-wave science in the high school classroom
Benjamin Farr a Northwestern University, Department of Physics & Astronomy, Evanston, IL 60208
GionMatthias Schelbert b Evanston Township High School, Science Department, Evanston, IL 60202
Laura Trouille c Northwestern University, Center for InterdisciplinaryExploration and Research in Astrophysics, Evanston, IL 60208
Abstract
This article describes a set of curriculum modifications designed to integrate gravitational-wavescience into a high school physics or astronomy curriculum. Gravitational-wave scientists are on theverge of being able to detect extreme cosmic events, like the merger of two black holes, happeninghundreds of millions of light years away. Their work has the potential to propel astronomy into anew era by providing an entirely new means of observing astronomical phenomena. Gravitational-wave science encompasses astrophysics, physics, engineering, and quantum optics. As a result, thiscurriculum exposes students to the interdisciplinary nature of science. It also provides an authenticcontext for students to learn about astrophysical sources, data analysis techniques, cutting-edgedetector technology, and error analysis. . INTRODUCTION Today the vast field of astronomy exists almost entirely within one medium of observation:electromagnetic radiation. From radio waves to gamma rays, the electromagnetic spectrumhas provided us with the observational data necessary to reach our current understanding ofthe universe. However, this restricted view of the universe has provided us with a relativelylimited knowledge of objects that emit little to no light, such as black holes and neutronstars. To better observe these bodies, we must look to an alternative cosmic messenger.The Laser Interferometer Gravitational-wave Observatory (LIGO) and partner observatoryVirgo are on the verge of making the first direct detection of gravitational waves, whichwill provide astronomers with the most direct observations of black holes yet.This cutting-edge field was brought into the high school classroom as part of the GraduateSTEM Fellows in K-12 Education (GK-12) program, funded by the National Science Foun-dation. Authors B. Farr (GK-12 fellow and LIGO Scientific Collaboration member) andG. Shelbert (GK-12 partner and astronomy teacher) spent the 2010–2011 academic yeardeveloping and integrating lessons based on gravitational-wave science into the high schoolastronomy curriculum, under the guidance and mentorship of L. Trouille (GK-12 mentor).The course had no prerequisites, and students’ math proficiency ranged from basic algebra tomultivariate calculus. However, most of the students had never heard of gravitational-wavescience and therefore started with the same prior knowledge of the subject. Students werefascinated by the concept of gravitational waves and colliding black holes, which resultedin significant self-motivation. By explicitly connecting existing topics in the curriculumto gravitational-wave science whenever possible, these lessons gave coherency to units thatbefore may have seemed disconnected.The structure of this paper is as follows. In Section II we provide an introduction togravitational waves, detectors, sources, and data analysis techniques. Section III outlinesseveral examples of how we have incorporated gravitational-wave science into the high schoolastronomy classroom. 2 I. GRAVITATIONAL-WAVE SCIENCE
Gravitational-wave science is the study of small ripples in space and time emitted by theacceleration of massive bodies. In the following sections we provide background informationon the physics underlying the emission of gravitational waves (Section II A), the main detec-tion methods (Section II B), the astronomical phenomena our gravitational-wave detectorsare sensitive to (Section II C), and the main methods for data analysis (Section II D).
A. Gravitational waves
With his general theory of relativity, Einstein triggered the most significant advancementin our understanding of gravity since Newton. Einstein’s theory proposes that the dimensionof time can be treated much like our three spatial dimensions, which together constitutespacetime. This spacetime is influenced by the presence of mass in a way similar to astretched fabric holding a heavy object. When other massive bodies travel through thiscurved region of space, their motions deviate from the normally straight paths, like a ballrolling on a curved fabric. This analogy can be extended further by considering the rapidmovement of very massive objects on the fabric, which produces ripples traveling outwardfrom the bodies, as also happens in spacetime. These ripples produced by the accelerationof massive objects traveling through spacetime are gravitational waves, and they carry withthem a wealth of information about their source. As these gravitational waves propagate,they exert a periodic expansion and contraction of the spacetime they pass through indirections perpendicular to the direction of travel. To examine the effects of these waveslocally, consider a ring of particles floating in space, free of any external forces. As thewave passes, the distance along each axis undergoes periodic expansion and contraction ina fashion exactly opposite to that of the perpendicular axis (see Fig. 1(a)–(d)). The goalof gravitational-wave detectors is to measure these minuscule vibrations, with the hope oflearning more about their sources.
B. Gravitational-wave detectors
Currently the most sensitive operational gravitational-wave detectors are based on theMichelson interferometer, which uses the interference properties of light to make incredibly3 a) t = P/ t = P/ t = 3 P/ t = P FIG. 1. Time evolution of a ring of particles influenced by a passing gravitational wave, where P is the period of the wave. Each consecutive panel is a snapshot taken P/ precise measurements of distances. As shown in Fig. 2, these detectors split a coherentlight beam from a single laser into two beams. These two beams travel along different pathsbefore recombining and entering the photodetector. More specifically, the detector is setup in an ‘L’ formation, with a mirror suspended at the end of each arm. A laser emits abeam of light that is in phase , meaning the peaks and troughs of each light wave are aligned.This original beam of light is split by the beamsplitter. One beam is reflected off of onemirror while the other beam is reflected off of the other mirror. Once the two beams returnto the beamsplitter they recombine, with some light going back toward the laser while therest passes to the photodetector. The beam splitter has a reflective coating on one side ofit, which means that of the two possible paths the light could take to the photodetector,one has reflected from the glass side of the coating, and the other from the vacuum side.These two different cases of reflection will result in a 180 ◦ phase difference. If the distancestraveled by each half of the beam are equal (i.e., the arms are equal in length), the twolight beams will be exactly out of phase and cancel each other out, resulting in all lighttraveling back toward the laser and none reaching the photodetector. If instead one armis slightly shorter than the other, the light no longer exactly cancels out, and a nonzerolight intensity is measured by the photodetector. The intensity of this light measured atthe detector depends very sensitively on the phase difference of the two halves of the beam.Thus by monitoring the fluctuations in the intensity of exiting light, the difference in armlengths can be determined with incredible accuracy.4 IG. 2. Schematic diagram of the Michelson interferometer, showing the path of the light beamas it is split and then recombined before entering the photodetector. The dark line on the beamsplitter indicates the reflective coating, and beams reflected from different sides of the coating havea 180 ◦ phase difference. This setup is very similar to that used in gravitational-wave detectortechnology. This is the underlying principle for the detection of gravitational waves. The three largestdetectors in the world based on this design make up the LIGO-Virgo Collaboration (LVC).Figure 3 shows the LVC network, consisting of two detectors in the United States (locatedin Hanford, WA and Livingston, LA) with arm lengths of 4 km that make up the LaserInterferometer Gravitational-wave Observatory (LIGO), as well as Virgo, a 3 km detectorin Italy. C. Sources
According to the theory of general relativity, any mass that is accelerating in a waythat is not perfectly spherically or cylindrically symmetric will produce gravitational waves.Though this excludes some processes like the spherically symmetric pulsations of stars, itdoes include countless other events, ranging from the energetic collision of stars and blackholes to the less spectacular toss of a ball. 5 a) LIGO Hanford (b) LIGO Livingston (c) Virgo
FIG. 3. The LIGO-Virgo gravitational-wave detector network, consisting of (a) LIGO Hanford(Credit: LIGO Laboratory), (b) LIGO Livingston (Credit: LIGO Laboratory), and (c) Virgo(Credit: EGO). LIGO Hanford (Hanford, WA) and LIGO Livingston (Livingston, LA) both have4 km long arms, while Virgo (Cascina, Italy) has 3 km long arms.
Consider a system of two bodies, each about as massive as the Sun, orbiting aboutone another. As the bodies orbit, gravitational waves are emitted with a period that isproportional to that of the orbit . These waves carry energy away from the system. As theorbit loses energy, the separation between the two objects must shrink, thereby decreasingthe orbital period. Furthermore, as the bodies get closer together, the second time derivativeof the quadrupole moment varies more rapidly, resulting in an increase in the gravitational-wave amplitude. This increase in frequency and amplitude continues until the orbital radiusdecreases to the point of merger, where the two objects physically combine to form a singlebody. Until the time of merger the system is said to be in its inspiral phase , which is modeledfairly accurately by making small corrections to the non-general relativistic equations ofmotion. An example of a gravitational wave produced during the inspiral phase of such asystem is shown in Fig. 4(a). As discussed in Section III B, when presenting this in a highschool classroom setting, the explanation for why the amplitude increases is more qualitative.The focus is on the students appreciating the connection between the more extreme curvatureof spacetime as the bodies get closer together and the increase in amplitude of the signal.If we were to take the same system, but compress each object’s mass into a smallerradius, the inspiral phase would be prolonged. In this case the orbital radius is able to reacheven smaller values before these denser objects merge, thereby increasing the amplitudeand frequency reached by the gravitational wave before merger. Consequently only binarysystems containing the densest objects in the universe, namely neutron stars and black holes,6 .00 0.05 0.10 0.15 0.20 0.25 - ´ - ´ - ´ - Time H s L S t r a i n (a) Accurate Model - ´ - - ´ - ´ - ´ - Time H s L S t r a i n (b) Common Misconception FIG. 4. The two most common responses by students when asked to hypothesize what the grav-itational wave from a binary merger should look like. (a) A qualitatively accurate model, similarto the majority of student responses. (b) A model with constant amplitude, the most commonmisconception among students. are capable of producing gravitational waves at amplitudes and frequencies detectable bycurrent detectors.The fact that we have yet to detect a gravitational wave, despite being surrounded bysources, is due primarily to the “stiffness” of spacetime. The stiffness of spacetime refers tothe incredible amounts of energy in gravitational waves that are required to distort spacetimeto a degree we can measure with our detectors. A second major factor is the relatively lowamount of energy emitted in gravitational waves by systems in the first place. As an exampleof the latter, the amount of energy per second (power) radiated in gravitational waves bythe orbit of Jupiter around the Sun is 5200 watts. Even though this is the most energeticsource of gravitational waves in our solar system, the energy radiated in all directions eachyear by the orbit of Jupiter would only be enough to power a single typical household in theUnited States, , d meaning we must look for much more energetic events occuring outside ofour solar system. The stiffness of spacetime is apparent if we consider a gravitational wavejust barely detectable with current detectors, which periodically changes the difference inthe distances along the arms of the detector by at most 10 − m with a frequency of 100 Hz.Such a signal has a flux (power per unit area) of about 10 − W / m . This is approximatelythe same flux in visible light measured 300 meters away from a standard 60 watt light bulb.Thus even though these fluxes are equivalent, in the case of gravitational waves the signalis barely detectable with state of the art detectors, whereas with electromagnetic radiation7he signal is easily detected by the human eye. D. Data analysis
The LVC detectors shown in Fig. 3 are measuring changes in the difference of the distancesalong the arms that are orders of magnitude smaller than the diameter of a proton (approx-imately 10 − m), reaching sensitivities of 10 − to 10 − m. In addition to gravitationalwaves, such minute fluctuations in arm length can also be caused by many uninterestingsources, including seismic vibrations, local highway traffic, etc. With so many noise sourcescausing signals at comparable levels to those we are trying to detect, advanced data analysistechniques are necessary. Many of these techniques rely on having a reasonably accuratetheoretical model for the system emitting the gravitational waves, which provide the hy-pothesized signal that is then looked for in the data. As described in Section II C, the LVCnetwork is particularly sensitive to the mergers of black holes and neutron stars. The mainsearch algorithm for merger signals in the LVC uses the technique of matched filtering, inwhich we first construct a bank of possible signals, and then search the data for instancesof a statistically significant match to a signal in the bank. This method is very efficientat detecting possible signals in large amounts of data, but does a poor job of determiningsource properties of individual signals, such as the masses of the merging objects and wherein the sky the source is located. To accurately estimate these parameters, other algorithmsare required that are designed to analyze individual signals found by the main search al-gorithm. These codes are based on Bayes’ theorem, and extract the maximum amount ofinformation possible from the measured signal in the data, assuming the models used in thesearch accurately represent the signal in the data. III. GRAVITATIONAL-WAVE SCIENCE IN THE HIGH SCHOOL CLASSROOM
Over the course of the 2010–2011 academic year the authors worked to incorporate con-cepts and ideas from the field of gravitational-wave science into a high school astronomycurriculum. Curriculum changes and lessons were implemented across 8 classes of students,with each class having about 25 students. Each individual class had a mix of juniors andseniors, as well as non-honors and honors students. Throughout the year new lesson topics8ere added pertaining to gravitational-wave astronomy. Existing lessons were also modifiedand tied into gravitational-wave science (e.g., waves and interference), creating a commontheme for the year’s lessons.In Section III A we describe how we incorporated gravitational-wave science into the ex-isting unit on waves. In Section III B we present how we used gravitational waves as anintroduction to the basics of general relativity. We also describe the demonstrations, guidedinquiry, and manipulation of computational models that we designed and used in the class-room to support student learning of gravitational-wave science. In Section III C we discusshow we taught signal processing using Fourier techniques in the context of gravitational-wave science. Finally, in Section III D we provide a list of other tools for educators interestedin teaching gravitational-wave science and in Section III E we discuss future work.
A. Waves and interference
The physics of waves is relevant to both the gravitational waves themselves, and the designof the interferometric observatories built to detect them. Many properties of electromagneticwaves, such as amplitude, frequency, and polarization, are also relevant to gravitationalwaves. Since the Michelson interferometer is designed to utilize the properties of waveinterference, a tabletop interferometer is an ideal demonstration to supplement discussionof these topics (see Fig. 2). In this modified lesson on wave physics, we first reviewedtransverse waves and their properties in a mini-lecture, material that the students hadread the night before. After the review, students broke into small groups to work on anactivity, making use of an online applet that allowed students to manipulate overlappingwaves and observe their resulting superposition. After completing the activity, students wereshown a tabletop Michelson interferometer, and were introduced to how constructive anddestructive interference pertain to its design. By applying very slight pressure to a mirror ofthe device, students developed an appreciation for the extreme sensitivity of the instrument.Small changes in the interference pattern on the projection screen were observed even whenstudents lightly tapped on the table holding the device. On this particular apparatus therewas a knob that would move the mirror by very small amounts. This knob was rotatedback and forth as an exaggerated example of the effects of a gravitational wave on theinterference pattern, while emphasizing to the students that during a gravitational-wave9vent, it is the distance between the mirrors and splitter that is expanding and contractingcausing such an effect, not the physical movement of the mirrors. This mixture of hands-ondemonstrations and computational models provided the students with a variety of ways todevelop an understanding of wave physics.Though we did not do so in this particular demonstration, future lessons could be im-proved by embedding a photodiode in the screen, which would measure fluctuations in theinterference pattern. By feeding to a speaker the varying voltage output by the photodiode,the changes in the interference pattern can be heard. In particular this would make highfrequency periodic changes to the pattern much easier to observe. With this configurationwe can potentially show that these instruments are even capable of picking up vibrationscaused by speech, acting much like a microphone. B. General relativity and gravitational waves
To help students begin to grasp the concept of gravity in the framework of general rel-ativity, a large fabric sheet was used as a 3D representation of our 4D spacetime. Spheresof various masses were placed on the sheet to demonstrate how the presence of mass curvesspacetime. Rolling marbles near these massive objects then showed how this curvature actsin a way analogous to gravity. Before demonstrating each different scenario to the students,we asked for their predictions—what did they think would happen? In the first scenario,the sheet was empty and we gave a marble an initial velocity so as to send it in a straightpath across the sheet. In the second scenario, a massive ball was placed in the middle of thesheet and the marble was given the same initial velocity as in the first scenario. Since thephysics of objects on the fabric sheet is fairly intuitive to the students, they were able topredict that the marble’s motion would be deflected by the curvature caused by the massiveball on the sheet. The students were also able to predict that the marble’s trajectory woulddepend on its speed and distance of closest approach to the massive ball. To demonstratecircular motion of the marble around the massive ball (simulating, for example, the motionof planets around our sun), we found that it worked best to place the marble quite closeto the massive ball and give it a small initial transverse velocity. The final demonstrationwas the case of a binary orbit, with two massive balls orbiting one another. During thisdemonstration students were asked to look at the behavior of the sheet far away from the10inary system, so that they would observe the distant vibrations caused by the binary orbit.These vibrations, the students were told, were analogous to gravitational waves.Following this discussion, students worked in small groups on an activity designed toguide them through the scientific reasoning required to determine the basic characteristicsof a gravitational wave from a binary system. This activity, which has been made publiclyavailable, begins by having the students analyze a simple sinusoidal wave, measuring itsamplitude, period, and frequency. They were then asked to draw examples of waves whoseamplitudes and frequencies changed with time, to get them thinking about the possibilityof waves without a fixed amplitude and frequency. Students were then reminded that grav-itational waves carry energy, and thus a system emitting gravitational waves must be losingenergy. This situation is analogous to what they had just seen in the fabric sheet demon-stration, where instead of losing energy through gravitational waves the orbit lost energydue to friction. This loss of energy resulted in the orbital radius shrinking and the orbitalvelocity increasing, just as it does during binary evolution.The last part of the activity had students hypothesize what they believed a gravitationalwave from an inspiraling binary system should look like, then compare that to a morerigorous computational model. The applet used to interface with the computational model(provided for free by Wolfram Demonstrations ) displays the gravitational wave for a givenset of parameters describing the binary system. Slider bars then allow students to manipulatevarious parameters in the model (e.g., inclination, component masses, etc.), to investigatehow these parameters can affect the modeled waveform.This combination of visual demonstrations, guided inquiry, comparison and manipula-tion of computational models, and group discussion throughout is essential for having thestudents develop an accurate understanding of gravitational waves and overcome commonmisconceptions. We found that through the demonstration and the guided inquiry work-sheet, over 80% of students were able to predict and explain why the frequency of thegravitational wave will increase with time as the binary system inspirals. At this stage,however, only about half of the students were able to deduce that the amplitude of the wavewill also increase with time, producing qualitatively accurate models like the one shownin Fig. 4(a). The most common misconception was that the amplitude of the wave wouldremain constant with time, as illustrated in Fig. 4(b). Through manipulating the compu-tational model, students with the misconception recognized that the amplitude of the wave11oes in fact increase with time. However, even after this stage, many could not explainthe physical cause for this amplitude increase. Only through a final full class discussion,in which students with more accurate models explained in their own words why the am-plitude increases during the inspiral phase, did the remainder of the students understandthis aspect of the system. More specifically, the students explained to their peers that thecurvature of spacetime becomes more extreme as the massive objects move closer together(as seen in the fabric demonstration). As a result, we expect the strength of the gravita-tional wave (i.e., its amplitude) to also increase as the black holes approach one another (asseen in the computational model). The more accurate model thus shows both an increasein frequency and an increase in amplitude of the gravitational wave with time during theinspiral phase. This final discussion as well as the small group discussions were very lively.The students were clearly engaged and excited to explore and gain understanding of thiscutting-edge science. Additional lessons can later be used to show how such models arecrucial to gravitational-wave detection in noisy data. C. Signal processing
Signal processing is a skill common to many fields in observational science, but is oftennot taught, or even mentioned, until students are in college. By teaching about gravitationalwaves elsewhere in the curriculum, we were able to provide an authentic context in whichto learn about signal processing. Not only that, but we were also able to appeal to manystudents’ interest in music and music editing while doing so.With such high levels of noise, signal processing and data analysis for gravitational-wave detectors is a challenging task. One crucial tool in the search for any periodic signalin time-domain data is Fourier analysis. Rather than scanning the data for indicatorsof the detector arm length changing periodically as a function of time (something madeimpossible by the noise causing such similar periodic changes), Fourier analysis allows oneto transform the data to look at power as a function of frequency instead. When viewingdata in the frequency domain, the presence of a low-level periodic signal in random noise iseasily seen, even with signal amplitudes much smaller than that of the noise. In the contextof gravitational waves, a given waveform is generated according to a computational model.This model is then subtracted from the data, and the remaining data is compared to the12oise measured in earlier data that did not contain a measurable signal. How well these datawith the model signal subtracted match the previously measured noise gives a quantitativeway to assess how well the model matches the signal.Students used Audacity, an open-source audio editing program, to generate specifictone and noise spectra. They then added the tone and the noise spectra together. Fig-ure 5(a) shows the time-domain track of the combined data, containing white noise and alow-amplitude 100 Hz sinusoidal wave. By using Audacity, students were able to see that avisual inspection of the time-domain data does not allow them to separate the signal fromthe noise, nor can they hear the signal when playing the audio sample. The students thentook the Fourier transform of the composite track, as shown in Fig. 5(b). The spike cor-responds to the frequency of the input tone’s low-amplitude sine wave. This demonstratedto them how using Fourier analysis can aid in the search for a quiet (low amplitude) coher-ent signal buried in random noise. This is a problem very similar to that encountered ingravitational-wave data analysis. Time (s) −4−3−2−101234 L o u d n e ss ( A r b i t r a r y U n i t s ) (a) Time Domain Signal Frequency (Hz) L o u d n e ss ( A r b i t r a r y U n i t s ) (b) Frequency Domain Signal FIG. 5. Students used the open-source audio editing program Audacity to explore the use ofFourier analysis in signal processing. (a) A composite track containing white noise and a 100 Hzsine wave, generated by the student. (b) The result of a Fourier analysis of the combined signaland noise, showing the presence of a strong signal at 100 Hz.
Finally, students were shown a simulated noise spectrum of LIGO, seen in Fig. 6(a), andthe frequency-domain representation of a gravitational wave from a binary inspiral, shownin Fig. 6(b). Students were also able to listen to the audio representation of these data,13nd could distinctively hear the difference between white noise and LIGO’s noise, as well aslisten to the waves they had learned about in a previous activity (see Section III B). Frequency (Hz) -20 -19 -18 -17 -16 L o u d n e ss ( A r b i t r a r y U n i t s ) (a) Simulated LIGO Noise Spectrum Frequency (Hz) -39 -38 -37 -36 -35 -34 -33 L o u d n e ss ( A r b i t r a r y U n i t s ) (b) Spectrum of a Gravitational-wave Model FIG. 6. Since LIGO is most sensitive to frequencies around 100 Hz, noise and signals relevantto LIGO can be converted to sound data that is audible to the human ear. Using sound editingsoftware, students were able to listen to and plot the spectra of (a) simulated LIGO noise, and (b)a gravitational-wave signal from a binary merger.
D. Other tools for gravitational-wave education
As part of its education and public outreach efforts, the LVC has created many other toolsto assist with educating students about gravitational waves. The LIGO Science EducationCenter located on the Livingston, LA detector site hosts field trips and professional devel-opment workshops, as well as a Research Experience for Teachers program. This programis a six-week paid internship for K-12 teachers, designed to provide teachers with the oppor-tunity to work in a scientific research environment on topics related to LIGO. The Einstein’sMessengers website provides many curricular resources including connections to state andnational standards, teacher and student study guides, and classroom activities related toLIGO and gravitational waves. Lastly there are many web applets and games designed tointroduce students to concepts in gravitational-wave physics and detector technology. Thegwoptics.org website hosts outreach material, including several games developed by thegravitational-wave group in Birmingham, UK. Black Hole Hunter is a game intended to14ntroduce people to gravitational-wave data analysis, having them search for the sound ofgravitational waves in simulated noisy data. E. Future work
Now that basic gravitational-wave science has been integrated into the astronomy curricu-lum, more advanced topics can be introduced in coming years. For example, the additionof independent study projects would provide another way to engage student in hands-onactivities. One possible project would be to have a group of students design and build theirown interferometric detector. The components necessary to construct a tabletop interfer-ometer are relatively cheap, requiring only a laser, beamsplitter, photodiode, tabletop, andtwo mirrors. An optical table would be ideal to house the interferometer, though that couldbe quite expensive to obtain. Cheaper tables could be constructed from wood or other ma-terials, and table construction itself could even be part of the project. Once the detectoris built, students could experiment with ways of making it more sensitive and reducing theeffects of environmental noise.The material presented here was integrated into the astronomy curriculum throughoutthe year. Time should now be spent to condense this into a single self-contained unit thatcan be more easily inserted into a K-12 or introductory college physics curriculum.One main area still to be added to the unit is parameter estimation. After the detec-tion of the first gravitational wave, the era of gravitational-wave astronomy will begin. Inorder to extract all the information available from a gravitational-wave signal, one mustuse a technique specifically designed to do so. Some work has been done to bring param-eter estimation concepts into the classroom, however lessons focusing on the currentlyused Bayesian methods have yet to be developed. The Bayesian analysis techniques em-ployed by the LIGO-Virgo collaboration are designed to extract the physical characteristicsof the source of a measured gravitational wave. These methods utilize concepts fromcomputational science, statistics, applied math, and other disciplines. By including thisin the curriculum, students would be exposed to topics across the STEM fields that theywould normally never see in the high school setting, further demonstrating the importanceof interdisciplinarity in science. 15
V. SUMMARY
Gravitational-wave astronomers are on the verge of directly detecting gravitational wavesfor the first time. Within the next decade, gravitational-wave science will change the field ofastronomy by opening a new window to the universe. As gravitational-wave science assumesa more prominent role in the astronomical community, it will be important for people to haveat least a basic understanding of what gravitational waves are. This article has provided sev-eral examples of how to introduce students to waves, interference, gravity, general relativity,and basic data analysis techniques through their applications to gravitational-wave science.Through these interactive demonstrations and computationally based activities, students areable to learn about gravitational waves and the technology behind their detection, withoutlosing focus on topics already in the curriculum.
ACKNOWLEDGMENTS
This work was supported by the NSF GK-12 grant, award DGE-0948017, and the NSFLIGO grant, award PHY-0969820. The authors would like to thank the referees for theircomments and suggestions.
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