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• frequency ratio sampling/signal:... However, it is interesting to understand why there is such a large incidence of noise in figures 14 and 15 (when using the laptop computer) whereas when using the diapason (figure 11) there is a crisp peak at 440Hz and even the second harmonic is clearly noticeable at 880Hz, with the noise signal being dwarfed by an impressively distinct FFT peak. When using the signal generator, there is a very crisp peak at 2000Hz, and when looking at figure 15, this is not the case. It can be concluded that in terms of quality of disturbance, the diapason ranks first, followed by the signal generator and by the laptop computer, responsible for the most noise. From this, the idea of subtracting the noise spectrum from the other graphs, even when possessing matching folding frequencies, is invalid, as the noise is dependent on the source causing the disturbance.... Distance travelled by the mirror From figure (6) it can be seen that the reciprocal of the distance between the peaks gives the time it takes for one bright fringe to turn into another bright fringe, and this is directly proportional to the distance travelled by the mirror; to be able to achieve a clear peak to peak frequency, the mirror must have moved a full λ before coming back to its original position, or it must be moving with constant velocity for a distance Nλ before moving backwards. The occurrence of double peaks proves that the mirror effectively does move by λ as opposed to a distance Nλ because the regularity of the disturbance must be caused by a one off event, periodic with the oscillation of the mirror. The scenario of the perturbation occurring in regular steps of Nλ, thus dependent upon the mirror’s horizontal displacement is very unlikely. Hence, by analysing the disturbance it is possible to conclude that the mirror does indeed move a full λ in distance; the mirror moves 633nm per oscillation. The double peaks were removed by tweaking the mirrors making the central maxima form in the centre of the detector.... frequency 800Hz.txt... Proceeding When the tuning fork is hit, a sound wave will propagate through the air. This will cause compressions and expansions in the air, resulting in higher and lower density regions respectively. The density of particles is proportional to the refractive index, hence when shining a laser beam through this perturbed region, it will be affected by these fluctuations in refractive index. By looking at how such fluctuations affect the interference pattern produced on the screen one can extract important information such as the frequency of the sound wave.... FFT frequency The folding frequency[footnoteRef:4] is the step for which the FFT components are calculated, it is found by adding the folding frequency to each data point, starting from 0. Hence, the first FFT data point would be plotted to an x coordinate of 0, the second would be the folding frequency, the third would be two times the folding frequency and so on. According to the Nyquist theorem of sampling; the maximum frequency component that can be determined using a given dataset of points equally spaced t seconds apart is equal to 1/(2t). The folding frequency is therefore:... In a Michelson interferometer, light from a monochromatic source (S) is divided by a beam splitter (BS), oriented at an angle of 45° to the beam, producing two beams of equal intensity. The transmitted beam (T) travels to mirror M2 where it is reflected back to BS. 50% of the returning beam is then deflected by 90° at the beam splitter and is made to strike the detector (D). The reflected beam travels to mirror M1, where it is reflected. Again, 50% of the beam passes straight through the BS and reaches the detector. The Laser is a He-Ne laser, having a polarized wavelength of 633nm (red). The wave is coherent and monochromatic; since the beam is coherent, light from other sources will not interfere with the interference pattern. Mirrors provide a way for the beam to change its direction of travel, if M1 and M2 are misaligned, the recombination of the beams occurs at a different location in the BS, resulting in the formation of two signals on D which do not form an interference pattern. When working with laser light, a cube beamsplitter (CB) possesses the best combination of optical performance and power handling ,CBs avoid displacing the beam by being perpendicular to the incident beam. To achieve the best possible performance, CBs should be operated with collimated light as convergent or divergent beams will contribute unwanted spherical aberrations to the setup. A piezoelectric was connected to a signal generator and attached to M2. This acted as a test for the apparatus and allowed the mirror to oscillate at various frequencies. The distance travelled by M2 due to excitation of the piezoelectric was a secondary investigation inherent in the project. The detector used allowed the intensity of light hitting it to be recorded. When two or more waves interact with one another an interference pattern is produced. This pattern is a result of the phase difference between the waves. When the waves are in phase constructive interference occurs and the resulting amplitude of the two superimposed waves is a maximum, on a screen, this is seen as a light fringe. When the waves are π out of phase, destructive interference occurs and the resulting amplitude is 0, on a screen this is seen as a dark fringe.
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Data Types:
• Slides
• Tabular Data
• Dataset
• Document