# What are overtones and how do they relate to harmonics?

Problem 43. Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes?

a. After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe.

b. After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe.

c. After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe.

d. After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe.

e. After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe.

I was trying to solve this problem. However, the concept of overtone is ambiguous. A search on the web gives me that an overtone is any frequency higher than the first harmonic. How can I use that to answer this question?

• Hint: Pipes produce only sounds which are standing waves within them. It's not hard to deduce the frequencies (or "overtones") each pipe will produce from this. Sep 20, 2014 at 16:20
• I did list out the frequencies: for open-closed: 660, 1980, 3300, 4620... for closed-closed: 440, 880, 1320, 1760... I get no match... Sep 20, 2014 at 16:29