As Section 17.3 discusses, high-frequency sound waves

Chapter , Problem 23

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As Section 17.3 discusses, high-frequency sound waves exhibit less diff raction than low-frequency sound waves do. However, even highfrequency sound waves exhibit much more diff raction under normal circumstances than do light waves that pass through the same opening. The highest frequency that a healthy ear can typically hear is 2.0 3 104 Hz. Assume that a sound wave with this frequency travels at 343 m/s and passes through a doorway that has a width of 0.91 m. Determine the angle that locates the fi rst minimum to either side of the central maximum in the diff raction pattern for the sound. This minimum is equivalent to the fi rst dark fringe in a single-slit diff raction pattern for light. (b) Suppose that yellow light (wavelength 5 580 nm in vacuum) passes through a doorway and that the fi rst dark fringe in its diff raction pattern is located at the angle determined in part (a). How wide would this hypothetical doorway have to be?