Two loudspeakers are placed above and
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Two loudspeakers are placed above and below each other, as shown in the figure above, and driven by the same source at a frequency of 630 Hz. An observer is in front of the speakers (to the right) at point O, at the same distance from each speaker. (f) If the speed of sound is 343 m/s, what minimum vertical distance upward should the top speaker be moved to create destructive interference at point O?
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- Speakers A and B are 100 m apart and send out coherent sound waves with frequency of f = 200 Hz. Alice is standing at the center of the line that connects the two speakers. If she starts walking toward either of the speakers, (a) What is the shortest distance she should travel to hear two constructive interference? (not counting the one at the center of the line)(1) A 1024 Hz tuning fork is placed at the source position in the figure shown. What must be the smallest radius r such that a minimum will be heard at the detector? [Hint: Usound = 343 m/s.] (2) If the radius is kept fixed, what other frequencies would lead to a minima? source detectorTwo small slits are in a thick wall, 27.5 cm apart. A sound source from the behind the wall emits a sound wave toward the wall at a frequency of 2,000 Hz. Assume the speed of sound is 342 m/s. (a) Find the (positive) angle (in degrees) between the central maximum and next maximum of sound intensity. Measure the angle from the perpendicular bisector of the line between the slits. ° (b) The sound source is now replaced by a microwave antenna, emitting microwaves with a wavelength of 2.75 cm. What would the slit separation (in cm) have to be in order to give the same angle between central and next maximum of intensity as found in part (a)? cm (c) The microwave antenna is now replaced by a monochromatic light source. If the slit separation were 1.00 µm, what frequency (in THz) of light would give the same angle between the central and next maximum of light intensity? THz
- Two loudspeakers are mounted on a rack, one h = 2.74 m above the other. Exactly 8.00 meters to the right of the midpoint, a microphone rests at point O. Point O is equally distant from each loudspeaker. The loudspeakers are driven by the same tone generator and vibrate in phase at 390 Hz. It is possible to create a condition of destructive interference at Point O by changing one or both of the path lengths (r1 and r2) between speaker and microphone. Suppose that this is done by raising the upper speaker while leaving the lower speaker in place. What is the smallest vertical distance (in m) that you would need to raise the upper speaker by, in order to create destructive interference at Point O? (The speed of sound waves in air is 343 m/s.)A step-index fiber of radius a = 20 μm and refractive indices ?1 = 1.47 and?2 = 1.46 operates at ?0 = 1.55 μm . Using the quasi-plane wave theory andconsidering only guided modes with azimuthal index l = 1:(a) Determine the smallest and largest propagation constants.(b) For the mode with the smallest propagation constant, determine the radii of the cylindrical shell within which the wave is confined, and the components of the wavevector k at r = 5 μm.Radio waves from a star, of wavelength 204 m, reach a radio telescope by two separate paths, as shown in the figure below (not drawn to scale). One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is 0 = 24.0° above the horizon. Find the height of the cliff. (Assume no phase change on reflection. The image is not drawn to scale; assume that the height of the radio telescope is negligible compare to the height of the cliff.) m Direct path Reflected path Radio telescope