Real life wavelength problem

Question

While attending a music rehersal, 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 you do, you offer to find the blockage. The organ pipe is 2.0 m long, was open at both ends, and was originally tuned to a fundamental frequency of 128 Hz (C below middle C).

a. What is the wavelength of the fundamental?

b. If the note you now hear is closer to 262 Hz (middle C), where is the blockage with respect to the opening at the bottom of the pipe?

c. What is the speed of the wave of the pipe?

Answer 1

a) open-open pipe is half wavelength long therefore wavelength of fundamental is 4.0 m.

c) speed = frequency * wavelength = 512 m/s

b) with blockage, pipe is now open-closed and is quarter wavelength long

wavelength = speed/frequency = 1.95 m

so location of blockage = 1.95/4 = 0.49 m from bottom