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Revision:Waves 2TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Physics > Waves 11.1 Traveling waves11.1.1I assume what we're talking about here is
The value of
11.1.2This is effectively what I described in the SL bit...In case you forgot
11.1.3Huygens' principle - This is a geometrical representation of how waves move through media. Each wave front is assumed to be an infinite number of point sources, each radiating in a circle. After a given period of time, a new wave front is drawn along the edges of these radiated circles, and the process is repeated...to draw it on paper, start with a wave front, place a number of points, and from these, draw the waves being emitted as if each of these were a point source. This results in a series of circles, but obstructions can change this. Waves could be reflected or absorbed by an object, waves entering a medium of higher optical density will slow down (and so won't go as far). After a given period of time (depends on the speed of the wave), draw an new wave front running along the edges of these circles as appropriate for the situation. The process is repeated over and over until it gets so boring that you stop. This helps to explain some of the phenomena of waves...diffraction...a very thin slit will only have a single point source, and so it will radiate in a circle, or wraps around an object, but you really need to draw a diagram to see that...refraction...as it enters the more dense medium, the waves slow down, pulling the wave around, and so on. This model can be applied to any waves but they'll probably be light, water or sound.
11.1.4Partial reflection occurs when ever light changes media...when light goes from water to air, some light is reflected from the boundary, ditto going the other way. Total internal reflection occurs when light enters a boundary (from the more dense side) at an angle greater than the critical angle, and all the light is refracted back into the medium. This critical angle can be found by inserting 90 as the angle of refraction in Snell's law, thus creating
11.1.5 : Some examplesLight through optical fibers - This is used both as a communication system, and as a sort of camera in hard to reach places. Light is totally internally reflected through the glass core, which can be bent as long as the light passing through it does not exceed the critical angle (see optics for more info)
11.1.6Refractive index is dependent on the wavelength thus different wavelengths of light will be refracted different amounts through the same boundary. Short wavelength light will be refracted more, and long wave length less. This means that if white light is shone onto a prism, then the light can be separated out into it's component colors, red being refracted the least, and violet the most.
11.2 Interference and Diffraction11.2.1If, for example, we have two point sources producing waves in a circle, they will interfere differently at different points...the easiest way to do this is to draw circles out from the source representing the crests (Except now we can call this Huygen's principle)...when two of these coincide, constructive interference produces a bigger crest. When two gaps coincide, we get a bigger trough, when one crest and one trough coincide, there is destructive interference, and they add to zero. This allows the interference pattern, and the amplitude at each point to be found.
11.2.2For two sources to be coherent, they must emit the frequency waves, in the same phase (ie when one emits a crest, so must the other). Path difference is the difference between the distances of a certain point from each source. The the path difference is a multiple of the wavelength, then constructive interference (an antinode) is produced), if it's a multiple + 1/2 complete destructive interference occurs (producing an node), and points in between have something between a node and an antinode. The pattern produced is a series of lines pointing away from the point exactly between the sources, and alternating constructive-destructive-constructive out from the center.
11.2.3Light strikes the two slits, and then produces two coherent point sources next to each other. 1) Light striking the center of the screen has an equal path difference from both, and so produces a bright band on the screen level with the slit (since the light is spread over the smallest area). 2) Light traveling out at such an angle that the light from the top source must travel exactly 1/2 a wavelength further than the bottom one to reach the screen. this means they are out of phase, and annul on the screen. As we move further around, the path difference will be 1 wavelength, they will reinforce, and produce a bright band, and so on alternating.
where The
11.2.4Thin films - This is straight out of optics, so there might be too much detail...you decide.
11.2.5A diffraction grating is basically a series of slits, rather than two (as in young's double slit). These slits produce much more precise lines, because rather than just requiring two beams to coincide, they require many to do so. This produces a much sharper pattern, and is more easy to analyze. If white light goes through the diffraction grating, different frequencies will diffract different amounts, and so spectra will be produced. Like this, then, the component colors of light can be found, with there exact wavelengths (because is affects the angle at which the bright bands occur). Calculations can be done with where
11.3 Source/detector movement11.3.1Shock waves are generally formed when the source of sound waves is traveling above the speed of sound. as the plane (since it's usually a plane) approaches the speed of sound, the sound waves don't really get away form the plane, but rather build up in front of the plane. Over time, many of these waves constructively interfere, producing what is known as the sound barrier. Once the plane moves faster than this, the sound waves are left behind the plane, creating a shock wave, which follows under the plane. The angle of the shock wave can be found by taking one point to be the source, then finding where the source would have been 1 second ago. from this point, calculate how far the wave would have gone out from this point in that second, and draw in the circle. A line can then be drawn from the point to the edge of the circle (in a tangent). This will be at 90 degrees to a line from the center, and since two sides are known, the angle of the shock wave can be calculated.
11.3.2Doppler effect...This effect is seen by the change in frequency of sound when either the source or the observer are moving...this therefore affects the actual number of waves the observer hears per second, and so changes the observed frequency. If the observer and source are moving closer together, then more wavefronts will be observed per second, and so the frequency will be higher. If they are moving apart, then fewer wavefronts will be observed, and so the frequency will be lower.
11.3.3When the source is at rest, the distance between wave crests is lambda. The the frequency is If we then assume that the source is moving towards the observer at vs, then in time In the same time, the source has moved At time Therefore, the new wavelength will be
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse. , and since \displaystyle f' = \frac{V{\lambda '} = \frac{v}{(\lambda (1 - \frac{V_s}{V}))} 
If the motion is away from the observer, then
Thus, Since
(This is for an observer moving towards the source, a sign change will be necessary as above).
11.4 Standing waves11.4.4Nothing for this section - what goes here? Can anyone help out?
11.4.2An overall graph of a standing wave will look like a sine curve superimposed over a -sine curve. at any given point in time, though, consecutive antinodes will be on opposite sides, so if one is up, the next will be down, then up and so on. The nodes will divide the string into equal segments, and so calculations can be done with a sort of arithmetic sequence thing.
11.4.3Equation relating fundamental frequency to tension and mass per unit length.
This allows us to calculate the velocity of a wave in a given string based on This equation can be equated to: We can then play around with it, to get various formulae...for example,
11.4.4As I've said before, an open end in a pipe will have an antinode, and a closed end will have an node. Therefore, a closed-closed pipe will have a half wavelength, as will an open-open pipe, but an open-closed pipe will have one quarter. These are the fundamental frequencies, then half wavelengths can be added to get the first, then second and so on harmonics. Most of the problems involve relating the length to the wavelength / frequency of the sound produced.
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