Explore the principles of wave propagation and the Doppler effect through mathematical derivations and applications. From wavefronts to signal detection, this document delves into the intricacies of wave behavior.
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[...] We have and finally Yes so we have . Digital application (for m/s. This is a plausible speed to traverse the human body. . Digital Application: . The previous calculations for questions and are still valid. Digital Application: MHz We take up the expression of on which we perform a limited expansion: so and finally . In blue for and in red for . The signal detection is optimized for the largest (in absolute value). Therefore, the receiver must be placed in yes and yes . [...]
[...] (note : Exercice 2 Yes this is a solution to the wave equation then . So . We have . This is the dispersion relation. The exponential notation is: with . On a and so . so . so . We can finally write that: so . Using the decomposition of cosine and sine in exponential form, we also find: Original amplitude is and the original phase is . The temporal period is the smallest solution to the equation and . The Space Age is the smallest solution to the equation and . [...]
