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- 13. Two-point sources vibrate in phase at the same frequency. They set up an interference pattern in which a point on the second nodal line is 29.5cm from one source and 25.0 cm from the other. The speed of the waves is 7.5cm/s. a. Calculate the wavelength of the waves b. Calculate the frequency at which the sources are vibrating [2T] [2T]6. We have a signal x(n) = xa(t)]1=nT; t=nT1 where T1 7 msec, and we wish to convert x(n) to y(m) such that y(m) = xa(t)]t=mT2 with T, = 5 msec. Develop a system to do this, being sure to specify the frequency re- sponse of any filters that are used (ideal responses are okay). Are there any restrictions on xa(t) that should be imposed so that this is possible?2. Unpolarized light of intensity 100 mW/m² passes through two filters. The first filter has an alignment of 30.0 degrees from the vertical. The intensity of the light that passes through the second filter is 41 mW/m². What is the angular alignment of the second filter with respect to the vertical? [2] A. 5° B. 10° C. 15° D. 20° E. 25° F. 30° 3. Which waves travel slowest in vacuum? [1] A. red light B. blue light E. They all travel with the same speed. C. x-rays D. gamma-rays 4. Point out the incorrect statement with respect to an electromagnetic wave in vacuum (or air) [2]. A. The color depends on the wavelength. B. The energy is transported with speed c in the direction of propagation. C. Both the electric field and the magnetic field exist in a plane perpendicular to the direction of propagation. D. The electric and the magnetic fields change in time, but do not change with position in space. E. The electric field vector and the magnetic field vector are always perpendicular to each…
- 2- If the function describing the change in the electric field and magnetic field in a non-conducting medium is given by: E= E, cos (@t-kz) i , H= H, cos (@t-kz) j Use Maxwell's equation derived from Faraday's law to find the transverse impedance n and then find the impedance if the wave propagates in a vacuum.8. A 26m wavelength of a radio wave is produced by two sources simultaneously. The interference of these two waves are observed at a point on a line perpendicular to the source. The sources are at a distance 78 and 143m away from the point of observation. Describe the nature of interference at the point and also find the order of the max/min reception at that point.2. Show, provided c= /k, then E = Eo sin(kx - wt) is a solution to the wave equation: where the operator 7² = V²E 2² 0x² = î+ 1 0²E c² at² 2² 2² + ·k dz² dyzî.