Two speakers sit 4.0m apart. Each is playing the same pure tone, of a single frequency...

 

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Two speakers sit 4.0m apart. Each is playing the same pure tone, of a single frequency sinusoidal sound wave. For simplicity, we can place these on the y-axis at y = +2.0m and at y= -2.0m. You stand on the centerline between the speakers, and 10.0m in front of them (this would be at y = 0m, x = 10.0m) At this location, you hear maximum intensity sound, a.k.a. constructive interference. You then walk in the +y direction until you hear a minimum intensity of sound, a.k.a. destructive interference. This happens when you reach y = 2.5m. (Your coordinates would now be x = 10.0, y = 2.5.) If the speed of sound is 340m/s, what frequency are the speakers playing? 1) Start by plotting out the locations of the speakers and the two points where the observer stands in the problem. 2) Interference is based on path length differences form different sources to the same detection point. Identify the paths from the two different speakers to the first observation point (10,0). How long is each of these paths? 3) Identify the two paths from the speakers to the second observation point, (10, 2.5). How long is each of these paths? What is the path length difference, 8, between them? 4) If this is the first place off the centerline where the observer encounters destructive interference, what can we conclude about how the path length difference, &, relates to the wavelength, ? 5) Find the wavelength of the sound waves. Then find their frequency. 6) Is this frequency in the range of human hearing? Two speakers sit 4.0m apart. Each is playing the same pure tone, of a single frequency sinusoidal sound wave. For simplicity, we can place these on the y-axis at y = +2.0m and at y= -2.0m. You stand on the centerline between the speakers, and 10.0m in front of them (this would be at y = 0m, x = 10.0m) At this location, you hear maximum intensity sound, a.k.a. constructive interference. You then walk in the +y direction until you hear a minimum intensity of sound, a.k.a. destructive interference. This happens when you reach y = 2.5m. (Your coordinates would now be x = 10.0, y = 2.5.) If the speed of sound is 340m/s, what frequency are the speakers playing? 1) Start by plotting out the locations of the speakers and the two points where the observer stands in the problem. 2) Interference is based on path length differences form different sources to the same detection point. Identify the paths from the two different speakers to the first observation point (10,0). How long is each of these paths? 3) Identify the two paths from the speakers to the second observation point, (10, 2.5). How long is each of these paths? What is the path length difference, 8, between them? 4) If this is the first place off the centerline where the observer encounters destructive interference, what can we conclude about how the path length difference, &, relates to the wavelength, ? 5) Find the wavelength of the sound waves. Then find their frequency. 6) Is this frequency in the range of human hearing?