Question

A particular organ pipe can resonate at 264 Hz, 440 Hz and 616 Hz, but not any other frequencies in between.

a) What is the fundamental frequency of this pipe.

b) Show why this is an open (at both ends) or closed ( one end open, one end closed) pipe.

Answer 1

Open pipes resonate at frequences f, 2f, 3f, 4f, etc ; closed pipes resonate at frequences f, 3f, 5f, 7f, etc. The difference in frequences is f for an open pipe and 2f for a closed pipe.
If pipe can resonate at 264 Hz, 440 Hz and 616 Hz, then
440 Hz - 264 Hz = 176 Hz
616 Hz - 449 Hz = 176 Hz
This isn't an open pipe because the frequences are not multiples of 176 Hz . Therefore, it is a closed pipe with fundamental frequency f = 176 Hz /2 = 88 Hz.
The frequecies of organ pipe are:
88 Hz, 3×88 Hz, 5×88 Hz, 7×88 Hz
Answer:
a) 88 Hz
b) it is a closed pipe