c please While attending a music rehearsal, the organist finds that one of the p

Question

c please

While attending a music rehearsal, the organist finds that one of the pipes in the organ has a blockage which results in an off key note being played. Realizing that you can help, knowing the physics that you do, you offer to find the blockage. The organ pipe is 2 0m long was open at both ends, and was originally tuned to play a fundamental frequency of 128 Hz (C below middle C) at a room temperature of 20 Celsius.. What is the wavelength of the original fundamental? If the note you actually hear is closer to 262 Hz, where is the blockage with respect to the opening at the bottom of the pipe (the sound is emanating from the top)? What is the explicit equation for both the waves (with and without the blockage)? You may assume that the maximum amplitude is 0.02. Graph the equation of the waves as a function of time.

Explanation / Answer

1. wavelength = 2L = 4 m
2. c = lambda*f
lambda = 344/262 = 1.3129 m
If blockage is t x m, then lambda = 4x
x = 0.3282 m
3. without blockage, y = 0.02*cos(2pi*x/lambda)
with blockage, y = 0.02*cos(2pi*x/4*0.3282)

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