Frequency of an open/closed pipe

[gmmstr827]

Homework Statement

A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or closed pipe. (b) What is the fundamental frequency of this pipe?

Homework Equations

Open pipe: f_1 = f_n+1 - f_n
Closed pipe: f_1 = (f_n+1 - f_n)/2
n = f_n / f_1

The Attempt at a Solution

Open:
f_1 = 616 - 440 = 176 Hz >>> n = 440/176 = 2.5
f_2 = 440 - 264 = 176 Hz >>> n = 264/176 = 1.5

Closed:
f_1 = (616 - 440)/2 = 88 Hz >>> n = 440/88 = 5
f_2 = (440 - 264)/2 = 88 Hz >>> n = 264/88 = 3

So I assume the pipe is closed because I got odd integer values for the harmonics in the closed pipe test, however, I'm not sure that I technically proved it to not be open.

It would have a base frequency of 88 if it is a closed pipe, or of 176 if it is an open pipe.

How can I improve my work/answer?

 

[ehild]

The solution is correct, only you should be more positive when choosing between closed an open. The values fn/f1 have to be consecutive integers. It is true if you suppose that the pipe is closed, but fails if supposing an open pipe. The pipe can not be open.

ehild