The drawing shows a loudspeaker A and point C, where a listeer is positioned. A second loudspeaker B is located somewhere to the right of A. Both speakers vibrate in phase and are playing a 51.0-Hz tone. The speed of sound is 348 m/s. What is the closest to speaker A that speaker B can be located, so that the listener hears no sound? Number i 4.01 Units m 60.0 First, recognize that the path difference will be equal to one-half of the wavelength, which can be determined by dividing the speed of sound by the frequency. Second, solve for the distance from speaker B to the listener. Third, use the Law of Cosines to set up a relationship between the distances from the speakers to the listener and the distance between the speakers themselves. Fourth, substitute the expression for the distance from speaker B to the listener into the Law of Cosines and simplify. Fifth, use the Quadratic Formula to solve for the distance between the two speakers. Lastly, use the given numeric values to determine the final answer.

The drawing shows a loudspeaker A and point C, where a listeer is positioned. A second loudspeaker B is located somewhere to the right of A. Both speakers vibrate in phase and are playing a 51.0-Hz tone. The speed of sound is 348 m/s. What is the closest to speaker A that speaker B can be located, so that the listener hears no sound? Number i 4.01 Units m 60.0 First, recognize that the path difference will be equal to one-half of the wavelength, which can be determined by dividing the speed of sound by the frequency. Second, solve for the distance from speaker B to the listener. Third, use the Law of Cosines to set up a relationship between the distances from the speakers to the listener and the distance between the speakers themselves. Fourth, substitute the expression for the distance from speaker B to the listener into the Law of Cosines and simplify. Fifth, use the Quadratic Formula to solve for the distance between the two speakers. Lastly, use the given numeric values to determine the final answer.

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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Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is useful in determining where low frequency sound is originating from. (a) Suppose a low-frequency sound source is placed to the right of a person, whose ears are approximately 18 cm apart, and the speed of sound generated is 340 m/s. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear? (b) Assume the same person was scuba diving and a low-frequency sound source was to the right of the scuba diver. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear, if the speed of sound in water is 1500 m/s? (c) What is significant about the time interval of the two situations?
You are working at an open-air amphitheater, where rock concerts occur regularly. The venue has powerful loudspeakers mounted on 10.6-m-tall columns at various locations surrounding the audience. The loudspeakers emit sound uniformly in all directions. There are ladder steps sticking out from the columns, to help workers service the loudspeakers. Many times, audience members break through the protective fencing around the columns and climb upward on the columns to get a better view of the performers. The upcoming concert is by a group that states that several very-high-volume pulses of sound occur in their concerts, and these sounds are part of their artistic expression. The amphitheater owners are worried about people climbing the columns and being too close to the loudspeakers when these peak sounds are emitted. They do not want to be held responsible for injuries to audience members ears. Based on past performances of the group, you determine that the peak sound level is 150 dB measured 20.0 cm from the speakers on the columns. The owners ask you to determine the heights on the columns at which to mount impassable barricades to keep people from getting too close to the speakers and hearing sound above the threshold of pain.
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