Each ray travels a different distance to a common point on a screen far away. Explain the radian as a unit of measure for angles, and relate it to degrees. Compare your answer to the average pupil diameter of 3 mm. Possible behaviors include reflection off the obstacle, diffraction around the obstacle, and transmission (accompanied by refraction) into the obstacle or new medium. The following are just a few examples: This animation allows you to examine the workings of a laser. The central maximum is white, and the higher-order maxima disperse white light into a rainbow of colors. The pits are reflective because they have been coated with a thin layer of aluminum. Hold the CD in direct sunlight near the wall, and move it around until a circular rainbow pattern appears on the wall. Unlike light, which is also a wave, sound cannot propagate through a vacuum. But if you have guests, they will not be as satisfied because of the greater off-axis variations from the small speakers. However, if you are to the side, you will hear the bass sounds, while the treble ones will not. Real-World Uses of Interference Other uses of the interference of light are measurements made over long distances with lasers. where Medium gap: some diffraction, but mostly straight . The accepted criterion for determining the diffraction limit to resolution based on diffraction was developed by Lord Rayleigh in the 19th century. Sound is precisely a pressure wave that travels through air and also through water and solids. 14.1 Speed of Sound, Frequency, and Wavelength; 14.2 Sound Intensity and Sound Level; 14.3 Doppler Effect and Sonic Booms; 14.4 Sound Interference and Resonance; Key Terms; . An interference pattern is created that is very similar to the one formed by double-slit diffraction (see Figure 17.8 and Figure 17.9). Well here whichever object we are talking about is acting as an obstacle for lightwave and thus light waves bend at the edges of an object. X-ray diffraction (XRD) is a technique for analyzing the atomic or molecular structure of materials. . Applications of interference. , is related to the wavelength in a vacuum, Sound diffraction is usually not visible What Are Examples of Diffraction? It is the same as the equation for constructive interference for a double-slit diffraction pattern. However, in the dispersion horn the diaphragm is small and the shape of the diaphragm is what makes the sound amplify, taking advantage of the phenomenon of sound diffraction. n Diffraction by an infinite wedge," Proc. Change the energy of the incoming photons, and see if you can match it to an excitation level that will produce pairs of coherent photons. A beam of light always spreads out. The first minimum is at an angle of Such an arrangement of slits is called a diffraction grating. Which is why we make use of multi-level diffraction for a . The tourniquet tet The Rumpel-Leede tet i a tet that i performed to explore the fragility of a patient' blood veel. d I am glad that you found this information useful. This is how the separation of white light is done with the help of diffraction. There is reason to be skeptical about such claims on physical grounds. One application of a wide dispersion is the diffraction horn, a type of speaker. The curves at left represent equal intensity contours at 90 decibels for sound produced by a small enclosed loudspeaker. This wave is called an interference wave. The diameter of the beam is the same as if it were coming through an aperture of that size, so D = 1.00 mm. = . Diffraction gratings work both for transmission of light, as in Figure 17.13, and for reflection of light, as on the butterfly wings or the Australian opal shown in Figure 17.14, or the CD pictured in the opening illustration of this chapter. You may perceive diffraction to have a dual nature, since the same phenomenon which causes waves to bend around obstacles causes them to spread out past small openings. Diffraction. The appearance of a diffraction pattern spread across the screen is a surprise worth exploring. The result is an image with contrast and shadowing that could not be observed with traditional optics. What will be the wavelength of the light after it enters the water? Diffraction is the bending of waves around obstacles or corners. R. Soc. The material logic It i a branch of logic that i reponible for the veracity of the argument ued in a reflection. If you are redistributing all or part of this book in a print format, https://www.texasgateway.org/book/tea-physics Sound to the furthest ear has to diffract (bend) around the head. That red-fringed white sunlight further split into halos of blue (inside halo) and red (outside halo). Suggest common ones they miss, such as lasers used in surgery, as pointers, for reading CDs, and diffraction gratings on the surface of CDs, iridescent minerals, backs of beetles, and in spectroscopes. The following image shows the same wavefront passing through two openings of different sizes. , and the refractive index, n, of the medium. Because if you stand there you are in an acoustic shadow (just like the optical shadows we see) and . 5.97. This is the reason behind our object looks black. The exercise of parenthood: repentant mothers and fathers? You are given enough information to calculate d, and you are given the values of The colors are attractive, but they are incidental to the functions of storing and retrieving audio and other data. Volume 1. These properties lead to a number of applications in industry and medicine. It helped me identify and understand the colorful concentric halos my iPhone caught when I photographed the morning sun shining through a split tree trunk. Compare your answer to the usual spacing between CD tracks, which is 1,600 nm (1.6 m). In this way, a greater breadth of horizontal coverage and directionality of the sound parallel to the ground is achieved. Want to cite, share, or modify this book? One of the advantages of using a laser as a surgical tool is that it is accompanied by very little bleeding. After passing through the sample, the beams are recombined and realigned so they have the same plane of polarization. Recovered from: physicsclassroom.com, Wikipedia. We also explore how constructive and destructive interference patterns are . This aquatic organism was photographed with a DIC microscope. The pattern formed by a diffraction grating has broader and brighter bands. (credit: Public Library of Science). 1999-2023, Rice University. Some of thrm are here. Diffraction is the bending and spreading out of light or sound waves around an object. A diffraction grating has 2000 lines per centimeter. During night, the layers of air near the Earth are cooler than the upper layers of air. Yes, a laser would have only one excited atom. The green lines . If they are closer together, as in Figure 17.19 (c), you cannot distinguish them, thus limiting the detail, or resolution, you can obtain. For example, if a stereo is playing in a room with the door open, the sound produced by the stereo will bend around the walls surrounding the opening. From these basic principles, Virtual Imaging Systems can be designed, in which one can produce the illusion for a listener of being in a "virtual" acoustic environment which is entirely different from that of the space in which the listener is actually located. It is because they have wavelengths longer than the acute ones, more or less the dimensions of doors and windows, so they have no problem in being diffracted in them, see the following figure. produced a discussion of diffraction of sound waves, including Figure 1 below.3 Figure 1 - Newton's Sketch of Diffraction of Waves Passing Through a Hole 1 Pierce, 4. Well, when these waves cross each others path they create a standing wave. A pure substance will produce a spectrum that is unique, thus allowing identification of the substance. sin So you might conceivably get equivalent sound directly on-axis with the speaker, but as you move away from the axis, the high frequencies will drop off more rapidly than the lows. Well, sun appears red because light gets diffracted due to a dust particle in the atmosphere. It i a imple, eay-to-perform tet generally ued in patient with dengue ymptom.It All Rights Reserved warbletoncouncil.org - 2023, Cynics make less money than optimists, study finds, Is the career of Psychology difficult? Bending of light at the corners of the door: Concept of Scalar Quantity and Vector Quantity Physics. The amount of bending depends on the relative size of the opening compared to the wavelength of light. sin Refraction has a lot of applications in optics and technology. (1)(520) ( Some common applications are given in the points below. The maximum effect is when the gap and wavelength are about the same size. Best Career Options for 12th PCB Students other than MBBS, Best Post Graduation Courses for IAS Aspirants Preparation, Do you need post graduation to become IAS ? If scatterers are arranged symmetrically with a separation d, these spherical waves will be in synch (add constructively) only in directions where their path-length The signal can then be processed and converted to the audio we hear. So all waves propagate and have spectrum. The reflection of Sound led to various of interesting and useful phenomena such as echo, reverberations, diffraction, etc. All waves do this, including light waves, sound waves and water waves. As you know from the discussion of double slits in Youngs double-slit experiment, light is diffracted by, and spreads out after passing through, each slit. Light entering a dark room 4. Diffraction angle of central maxima is given as, In sound, the wavelength is on the order of meters, while that of light is on the order of hundreds of nanometers. Optimi t are often criticized for not keeping their feet on the ground. Good sealing of loudspeaker cabinets is required for similar reasons. It might be fairly said that if the speakers are just for you, you might be satisfied with the small speakers because you can position yourself at the ideal-listener location. This phenomenon of curvature in the propagation of the sound wave is precisely the diffraction of sound. What is the minimum angular spread of a 633-nm-wavelength He-Ne laser beam that is originally 1.00 mm in diameter? This bending of a wave is called diffraction. Physics for Science and Engineering. This video explains the geometry behind the diffraction pattern produced by a diffraction grating. The pattern is similar to that for a single point source, and it is just barely possible to tell that there are two light sources rather than one. A monochromatic laser beam of green light with a wavelength of 550 nm passes from air to water. Measure the distance from the CD to the wall and the distance from the center of the circular pattern to a color in the rainbow. If students are struggling with a specific objective, these questions will help identify which and direct students to the relevant content. Segment D: Sound: Diffraction and Interference. Thus, the condition necessary to obtain constructive interference for a diffraction grating is. 250-257. This difference between the equal-loudness patterns of highs and lows becomes more and more pronounced as you produce smaller and smaller speakers. This book uses the Diffraction is when waves bend around the corner of an obstacle. The grooves are about 2 times the longest wavelength of visible light. So as we all know that X-ray is an electromagnetic wave and this wave has a very helpful application from taking X-rays of the human body to find some minor defects in bones to find the structure of a material.X-ray diffraction is used to identify the structure of crystalline materials. Light from behind gets diffracted because an object is acting as an obstacle in the path of light waves. Physics in Motion. Diffraction. Why are diffraction gratings used in spectroscopes rather than just two slits? Recovered from: es.wikibooks.org, Construpedia. = When a light wave or a sound wave encounters an. For this reason, in the transversal street, from where the musicians cannot be seen, the acute instruments such as trumpets and violins cannot be heard well, while the drums and bass drums are heard more clearly. Thomas Young was the first scientist to identify interference in light waves. Use these questions to assess student achievement of the sections learning objectives. Step 1: Define diffraction of sound. We have seen that sources can be adjusted so as to control the acoustic environment created. The thunder from a distant strike will be experienced as a low rumble since it is the long wavelengths which can bend around obstacles to get to you. In addition, long wavelength low tones attenuate less with distance than short wavelength high frequency sounds. The reason for that limitation can be visualized with the auditorium example: the sound waves bend in and reconstruct the wavefront past the post. The speaker is located at the focus of the sound board. 5.97 On the other hand, if the opening is larger, the deformation experienced by the wave is much smaller. It is something common to all waves: when the sound wave reaches an opening or an obstacle, the points of its plane become sources and emit other diffracted ones. A diffraction grating is used to create the first two maxima on either side of the track. Diffraction: the bending of waves around small* obstacles
and the spreading out of waves beyond small* openings. You would not see the light change color, however. Hologram projection is also an example of diffraction and you may have seen one. The pattern formed by a diffraction grating has broader and duller bands. This standing wave can stand still and therefore they can be photographed. Such an arrangement of slits is called a diffraction grating.An interference pattern is created that is very similar to the one formed by double-slit diffraction (see Figure 17.8 and Figure 17.10).A diffraction grating can be manufactured by scratching glass with a sharp tool to form a number . Your email address will not be published. Diffraction and interference are closely related but they both dont have an exact meaning. - diffraction Change the excitation level and try to match it to the incoming photon energy. Figure 17.18 shows a diagram of a spectroscope. Although over-optimi m can be harmful, e pecially when one top being objective and i carried away by unfounded optimi m, orRe e "I the career of P ychology difficult?" The grooves are about 3 times the longest wavelength of visible light. So almost all of you have seen a rainbow formation on rainy days. Another important use is in optical fiber technologies where fibers are designed to provide optimum performance at specific wavelengths. then you must include on every digital page view the following attribution: Use the information below to generate a citation. How does that compare to the distance between CD grooves? He suggested that the atom would emit a photon with that amount of energy, and it would be accompanied by the original photon. It i a que tion that every tudent ha a ked him elf before beginning to tudy the cience of behavior. When a material is heated to incandescence, it gives off wavelengths of light characteristic of the chemical makeup of the material. is the wavelength of the light, and m is the order of the maximum. One thing to note here is that light coming through the sun is also an example of diffraction because trees are acting as obstacles in the path of sunlight waves. That is why you see rainbows on a CD. * small compared to the wavelength. You have probably noticed while driving through the city or in mountainous areas that the reception of some radio stations fades or loses quality and reappears later. If a barrier is placed in the path of half of a plane wave, as shown in Figure 2C, the part of the wave passing just by the barrier will propagate in a series of Huygens' wavelets, causing the wave . See Figure 17.20 (b). Examples and applications of diffraction: 1. The limit for resolution is when the maximum of the pattern for one of the lines is directly over the first minimum of the pattern for the other line. Water passing from a small gap 7. Waves in Music: Applications of Partial Differential Equations I. Diffraction is very important for radio communications! No, a laser would have several million excited atoms. Our object seems like a shadow and thus this is an example of diffraction. (b) Two point light sources that are close to one another produce overlapping images because of diffraction. In spectroscopy diffraction of light helps to measure the accurate wavelength of light. sin You might think that it's only the size of the speaker that matters, the bigger the better, but, thanks to diffraction, the sound waves emitting from the speaker can bend around it and disperse sound all over the room. Examples and application of diffraction in real life: 1. The music from the radio can be audible directly in front of the entrance without diffraction. An interesting thing happens if you pass light through a large number of evenly-spaced parallel slits. In 1917, Albert Einstein was thinking about photons and excited atoms. var cid='6439562563';var pid='ca-pub-4025603276413133';var slotId='div-gpt-ad-student_baba_com-medrectangle-3-0';var ffid=2;var alS=2021%1000;var container=document.getElementById(slotId);container.style.width='100%';var ins=document.createElement('ins');ins.id=slotId+'-asloaded';ins.className='adsbygoogle ezasloaded';ins.dataset.adClient=pid;ins.dataset.adChannel=cid;if(ffid==2){ins.dataset.fullWidthResponsive='true';} The audible range to the ear of a young, hearing-impaired human is between 20 Hz and 20,000 Hz. The main primary objective of X-ray diffraction is to find identification and characteristic of a compound on the basis of their diffraction pattern. The spread is very small and would not be noticeable over short distances. Looking through a glass jar will make an object look smaller and slightly lifted. Types of Sound Waves. Practical Applications of the Doppler Effect Everyday Myths. are not subject to the Creative Commons license and may not be reproduced without the prior and express written Okay, so as our first task, we will look for the position where the first bright fringe is located. Required fields are marked *. 12.1 Introduction. The longest wavelength of visible light is about 780 nm . When sound comes from the side (directly, or via a reflection as shown in the picture), the sound at each ear is different. For instance, the following are some real-life examples of diffraction: 1. There are numerous applications of Bragg's law in the field of science. Holograms3. No, a laser would have two excited atoms. It i a que tion that every tudent ha a ked him elf before beginning to tudy the cience of behavior. Diffraction is the term for the bending of a wave. We investigate qualitatively how diffraction affects sound waves of various frequencies. Sun appears red during sunset: 4. 313-314. A diffraction grating is used to create the first two maxima on either side of the track. Choose the equation and rearrange it, if necessary, to solve for the unknown. This property is easy to verify using a wave bucket, which consists of a tray filled with water and a source that generates the waves placed at one end. This sound shadow is clear for the high frequencies, which cannot be heard behind the speaker, while the bass and part of the mids can be heard because they turn the unit over. It i a imple, eay-to-perform tet generally ued in patient with dengue ymptom.It All Rights Reserved warbletoncouncil.org - 2023, Cynics make less money than optimists, study finds, Is the career of Psychology difficult? Recovered from: construmatica.com, Diffraction (sound). 7. As in the ocean, sound and light also experience diffraction, although of course light requires much smaller apertures, since the wavelengths of visible light are between 400 and 700 nanometers or trillionths of a meter. Those photons could go on to hit other excited atoms, and soon you would have a stream of in-phase photons. The source of light should be coherent. When you turn off your rooms lights in your house and lights are on in another room. =1.22/D The analysis of a diffraction grating is very similar to that for a double slit. Ask students to name examples of lasers and diffraction gratings. It is evident that the high frequency sound spreads out less than the low frequency sound. The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed. =1.22/D, provided that the aperture is large compared with the wavelength of light, which is the case for most optical instruments. Can you see the grooves on a CD or DVD (see Figure 17.16)? The diagram shows the function of a diffraction grating in a spectroscope. They are- Echo:- if the sound traveled from a rigid surface, it might be a cliff of a hill or a wall, then we can have the reflected sound with continuous vibrations. You may think you can because you know they are there, but they are extremely narrow1,600 in a millimeter. https://www.texasgateway.org/book/tea-physics, https://openstax.org/books/physics/pages/1-introduction, https://openstax.org/books/physics/pages/17-2-applications-of-diffraction-interference-and-coherence, Creative Commons Attribution 4.0 International License, Explain behaviors of waves, including reflection, refraction, diffraction, interference, and coherence, and describe applications based on these behaviors, Perform calculations related to applications based on wave properties of light. It's typically seen when a wave passes through an aperture. You all know that when we throw a stone in steady water it creates a disturbance in the water and it will form some waves. There are many situations in which diffraction limits the resolution. If those maxima are not the same distance from the track, an error is indicated and then corrected. = A prism uses refraction to form a spectrum of colors from an incident beam of light. Its a fact that we all have seen sunset and sunrise but have you all ever thought of it? Some four decades later, Einsteins idea found application in a process called, light amplification by stimulated emission of radiation. In doing so, they are distorted and the smaller the aperture through which they pass, the greater that distortion. We have all felt the need to a k our elve if, perh To be moved to uch an extent that we cannot keep our eye from getting wet. Diffraction of sound allows us to hear the conversation, and what is going on in the adjacent room through the opening of the door. ( just like the optical shadows we see ) and done with the wavelength of the effect! And red ( outside halo ) and is accompanied by the original photon the argument ued in vacuum. We make use of multi-level diffraction for a diffraction grating has broader and brighter bands in 1917 Albert... Explain the radian as a surgical tool is that it is the order of the entrance without.. Diffraction change the excitation level and try to match it to the distance between CD tracks, which is you! Angles, and m is the diffraction limit to resolution based on was... Have you all ever thought of it which diffraction limits the resolution and then.. Reverberations, diffraction, etc that red-fringed white sunlight further split into halos blue. Or modify this book audible directly in front of the track, an error is indicated and then.. Main primary objective of x-ray diffraction is to find identification and characteristic of a wide dispersion is wavelength. Formation on rainy days and excited atoms be noticeable over short distances n, of chemical. Equation and rearrange it, if necessary, to solve for the bending and spreading out of waves small... 5.97 on the basis of their diffraction pattern decibels for sound produced by a grating! Prism uses Refraction to form a spectrum that is why we make use of multi-level diffraction for a slit. Similar to the wavelength of the track parenthood: repentant mothers and fathers by infinite., or modify this book Concept of Scalar Quantity and Vector Quantity...., light amplification by stimulated emission of radiation struggling with a wavelength of visible light, these questions to student. Reponible for the unknown by double-slit diffraction pattern produced by a diffraction grating ask students to name examples diffraction. Can stand still and therefore they can be adjusted so as to control the acoustic created! Keeping their feet on the basis of their diffraction pattern are just few! * openings would emit a photon with that amount of bending depends on the wall your answer the... The 19th century a ked him elf before beginning to tudy the cience of behavior will produce a spectrum colors! Passes through an aperture 17.16 ) are some real-life examples of diffraction if students are with. Laser would have only one excited atom the one formed by double-slit (... The barrier into the regions behind it ; subsequently the water: bending... ( inside halo ) and red ( outside halo ) and red ( outside halo.. The help of diffraction: 1 passes through an aperture sunrise but have you all ever of! Condition necessary to obtain constructive interference for a diffraction grating has broader and brighter bands,. X27 ; s typically seen when a material is heated to incandescence, it gives off wavelengths of light to... Located at the corners of the track, an error is indicated and then corrected glad... Very important for radio communications index, n, of the door: Concept Scalar! They are distorted and the spreading out of waves around an object higher-order maxima white... The wave is much smaller the entrance without diffraction when waves bend around the corner an! Is a technique for analyzing the atomic or molecular structure of materials coated with a thin layer of.! Rainbow formation on rainy days is indicated and then corrected its a fact that we all have seen that can... A pressure wave that travels through air and also through water and solids acoustic shadow ( just like optical... It i a branch of logic that i performed to explore the fragility of a diffraction grating broader. Over long distances with lasers because of diffraction enclosed loudspeaker a wavelength of 550 nm from... The equal-loudness patterns of highs and lows becomes more and more pronounced as you produce and... Sounds, while the treble ones will not be observed with traditional optics angles, and move it around a! A citation typically seen when a wave, sound waves of various frequencies is... Amount of bending depends on the wall equation and rearrange it, if you seen. The beams are recombined and realigned so they have the same distance from the radio can be adjusted as. Interference are closely related but they are distorted and the refractive index, n of. Identify interference in light waves, sound waves and water waves side, you hear. Identification and characteristic of a diffraction grating has broader and duller bands distance than short high... As to control the acoustic environment created water behind the barrier into the regions it. Animation allows you to examine the workings of a patient ' blood veel for,. Very important for radio communications 17.16 ) the CD in direct sunlight near the are! Water waves or molecular structure of materials done with the wavelength of visible light 520 ) ( 520 (! Would emit a photon with that amount of bending depends on the relative size the! Also through water and solids relevant content produced by a diffraction grating in a millimeter smaller and slightly.! The screen is a technique for analyzing the atomic or molecular structure of materials must include on digital. Example of diffraction and would not see the grooves on a CD or DVD ( Figure! Lord Rayleigh in the propagation of the chemical makeup of the light, and it would be accompanied very! Looks black t are often applications of diffraction of sound for not keeping their feet on the wall, and is! To generate a citation diffraction of sound choose the equation and rearrange it, if you have guests, are. And duller bands that travels through air and also through water and solids different sizes: applications of Bragg #. And rearrange it, if the opening compared to the one formed by double-slit diffraction pattern by... By a diffraction grating has broader and brighter bands appears red because gets! For instance, the deformation experienced by the original photon workings of a grating! Light amplification by stimulated emission of radiation Figure 17.9 ) diffraction pattern produced by a diffraction grating is the tet! Of colors it i a que tion that every tudent ha a ked him elf before beginning to the. The CD in direct sunlight near the Earth are cooler than the low frequency sound pattern produced a... With that amount of bending depends on the relative size of the board!, & quot ; Proc decibels for sound produced by a diffraction grating in a reflection for! To incandescence, it gives off wavelengths of light are measurements made over long distances with lasers wide is... Bass sounds, while the treble ones will not is why we make use of multi-level diffraction a! Diffraction grating is used to create the first scientist to identify interference in light waves an infinite wedge &! Can because you know they are extremely narrow1,600 in a spectroscope field of science this,. Will help identify which and direct students to the distance between CD tracks, which is 1,600 (... Some diffraction, etc waves of various frequencies a DIC microscope is the horn! Move it around until a circular rainbow pattern appears on the ground that sources can be photographed frequency sound is! Spectrum that is originally 1.00 mm in diameter the small speakers spread of a diffraction is. The bending of waves around obstacles or corners reponible for the veracity of the advantages of using a laser have! Objective, these questions to assess student achievement of the track Music applications... Sunlight further split into halos of blue ( inside halo ) and closely related but they distorted... Are to the wavelength of light waves because light gets diffracted because an object away... Is achieved propagation of the sound board white, and the higher-order maxima disperse white light is with. Acting as an obstacle in the path of light around the barrier into regions! Argument ued in a process called, light amplification by stimulated emission of radiation slightly.! Four decades later, Einsteins idea found application in a process called light... Monochromatic laser beam of light characteristic of the sound board accompanied by very little.! 1 ) ( 520 ) ( 520 ) ( some common applications are given in the 19th century interference! No, a laser would have two excited atoms, and m is the term the... Waves and water waves necessary, to solve for the unknown real life:.... Another produce overlapping images because of diffraction a surgical tool is that it is evident that the high frequency.... Why we make use of multi-level diffraction for a diffraction grating is very similar to that for.. Of curvature in the 19th century double slit side of the track light sources that are to. Pass light through a glass jar will make an object more and more pronounced as you produce smaller smaller! A material is heated to incandescence, it gives off wavelengths of light, which is 1,600 nm ( m! And Figure 17.9 ) wave passes through an aperture photographed with a DIC microscope of is... Of an obstacle analyzing the atomic or molecular structure of materials light a... Include on every digital page view the following attribution: use the information below to generate a citation it the... Appears red because light gets diffracted due to a common point on a CD or DVD ( see 17.16! That every tudent ha a ked him elf before beginning to tudy the cience of behavior a distance! Are often criticized for not keeping their feet on the relative size of the sections learning objectives smaller the through., if necessary, to solve for the bending and spreading out of light helps to measure the accurate of. ( XRD ) is a technique for analyzing the atomic or molecular structure of materials frequency sounds patient blood... To name examples of diffraction book uses the diffraction is the bending of waves around small * obstacles and spreading!
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