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.

icon
Related questions
Question
100%

Please help with part 1 in this question only, unsure how to draw out this problem. Thank you!

Written Challenge Problem, Sound Interference:
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 = Om, 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, 8, relates to
the wavelength, 2?
5) Find the wavelength of the sound waves. Then find their frequency.
6) Is this frequency in the range of human hearing?
Transcribed Image Text:Written Challenge Problem, Sound Interference: 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 = Om, 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, 8, relates to the wavelength, 2? 5) Find the wavelength of the sound waves. Then find their frequency. 6) Is this frequency in the range of human hearing?
Expert Solution
Step 1

We need to draw the arrangement as described in the Problem.

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer