Question

an organ pipe is open at one end and closed at the other end. if the wavelenght of the fundamental standing wave is .200m, what is the length of the pipe?

Answer 1

The length of an organ pipe open at one end and closed at the other, with a fundamental wavelength of 0.200 meters, is 0.050 meters (5 cm), since a closed pipe accommodates one-fourth of the wavelength for its fundamental mode of resonance.

Step-by-step explanation:

The length of an organ pipe that is open at one end and closed at the other end can be determined by understanding that the standing wave pattern in such a pipe will have a node (point of no displacement) at the closed end and an antinode (point of maximum displacement) at the open end. Since the wavelength (λ) of the fundamental frequency is given as 0.200 meters, we can relate it to the length of the organ pipe. For a pipe closed at one end, the fundamental wavelength is four times the length of the pipe (because the pipe represents ¼ of the wavelength in this mode).

Using the formula:

1. λ = 4L
2. 0.200 m = 4L
3. L = 0.200 m / 4
4. L = 0.050 m

Therefore, the length of the pipe is 0.050 meters or 5 cm.