Sound waves with frequency 4000 Hz and speed 350 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. The opening, which has a horizontal width of 31.0 cm, faces a wall 100 m away. Along that wall, how far from the central axis will a listener be at the first diffraction minimum and thus have difficulty hearing the sound?

Sound waves with frequency 4000 Hz and speed 350 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. The opening, which has a horizontal width of 31.0 cm, faces a wall 100 m away. Along that wall, how far from the central axis will a listener be at the first diffraction minimum and thus have difficulty hearing the sound?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 17P: A riverside warehouse has several small doors facing the river. Two of these doors are open as shown...

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A riverside warehouse has several small doors facing the river. Two of these doors are open as shown in Figure P27.17. The walls of the warehouse are lined with sound-absorbing material. Two people stand at a distance L = 150 in from the wall with the open doors. Person A stands along a line passing through the midpoint between the open doors, and person B stands a distance y = 20 m to his side. A boat o the river sounds its horn. To person A, the sound is loud and clear. To person B, the sound is barely audible. The principal wavelength of the sound waves is 5.00 m. Assuming person B is at the position of the first minimum, determine the distance d between the doors, center to center.
The entrance to a large lecture room consists of two side-by-side doors, one hinged on the left, and the other hinged on the right. Each door is 0.790 m wide. Sound of frequency 870 Hz is coming through the entrance from within the room. Take the speed of sound to be 340 m/s. What is the diffraction angle of the sound after it passes through the doorway when one door is open.
high-frequency sound waves exhibit less diffraction than low-frequency sound waves do. However, even high frequency sound waves exhibit much more diffraction 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 × 104 Hz. Assume that a sound wave with this frequency travels at 344 m/s and passes through a doorway that has a width of 0.95 m. (a) Determine the angle that locates the first minimum to either side of the central maximum in the diffraction pattern for the sound. (b) Suppose that yellow light (wavelength = 567 nm, in vacuum) passes through a doorway and that the first dark fringe in its diffraction pattern is located at the angle determined in part (a). How wide would this hypothetical doorway have to be?
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Multiple-Concept Example 3 reviews the concepts that are important in this problem. The entrance to a large lecture room consists of two side-by-side doors, one hinged on the left and the other hinged on the right. Each door is 0.690 m wide. Sound of frequency 757 Hz is coming through the entrance from within the room. Take the speed of sound to be 341 m/s. What is the diffraction angle 0 of the sound after it passes through the doorway when (a) one door is open and (b) both doors are open? e (both doors open) 0 (one door open) Units (a) Number Units (b) Number CEH
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