What Are the Frequencies of the First Two Overtones in a Closed Air Column?

[Exhonour]

Homework Statement

An air column closed at one end has a fundamental frequency of 500Hz. What are the frequencies of the first two overtones?

Answers:
1500Hz
2500Hz

Homework Equations

Overtone:
f = (n+1)f
n = overtone

Harmonic:
f = nf

The Attempt at a Solution

f1 = (n+1)f
= (1+1)500
= 1000Hz

f2 = (2+1)500
= 1500Hz
Im not getting it, what am I doing wrong? Its asking for frequency of overtone #1/overtone #2, I put the right values in the equation but I still don't get the right answer.

 

[hage567]

In a pipe closed at one end, only odd harmonics occur, so if the fundamental frequency is f₁, then the frequencies of the harmonics will be f_n = nf₁, where n = 3,5...

 

[baba89]

Your attempt at a solution is correct. The frequencies of the first two overtones are 1000Hz and 1500Hz, respectively. It is possible that the answer key or solution provided is incorrect, or there may be some other information missing that would change the calculation. It is always important to double check your work and make sure you are using the correct equations and values. If you are still unsure, it may be helpful to consult with a teacher or classmate for clarification.