The answers I got for this question is double what the book got. I'm not sure if it's the book that did something wrong, or if it's me. I tried a multitude of ways of working it out and got the same answer.
"An organ pipe is an air column closed at one end with an effective length of 75cm. The speed of sound inside the pipe is 330 m/s"
a. What is the frequency of the fundamental note produced by the pipe?
L=0.75m, n=1, v=330m/s
or
(Just noticed now that this is just a round about way of doing the first method of working out).
The textbook had 110Hz.
b. What is the frequency of the third harmonic?
n=3, L=0.75, 2L=1.5, v=300m/s
or
The textbook had 330 Hz.
c. What are the frequencies of the next two harmonics ... ?The pipe is closed at one end, therefore it can only produced odd-numbered harmonics.
The next two harmonics will be 5th and 7th.
and
The book had 550Hz and 770Hz.
I don't see any errors in my working out - unless I'm overlooking some important concept that requires something here to be divided by 2 due to the fact that the pipe is closed at one end. I don't think there is anything of the type though. If I did make an error, I suspect it would have been in part a - as I could have obtained the textbook answers if I had my fundamental frequency at 110 Hz using the ratio method of working it out.
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