Calculating Resonant Frequencies of Closed Air Columns

Click For Summary

Homework Help Overview

The problem involves calculating the resonant frequencies of a closed air column that is 60.0 cm long, using the speed of sound as 344 m/s. The original poster seeks to determine the frequencies corresponding to the first and second resonant lengths, while also noting a third resonant length mentioned in the textbook.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses confusion regarding the magnitude of the resonant lengths and how to initiate the calculations. Some participants point out the relevant equations and suggest resources for further understanding. There is also mention of the textbook's provided answers for multiple resonant lengths, which raises questions about the calculations leading to those results.

Discussion Status

The discussion includes attempts to clarify the equations involved and the relationships between resonant lengths and frequencies. Some participants have provided insights into the calculations, while the original poster acknowledges a better understanding after engaging with the responses. However, there remains uncertainty about the calculations for the first and second resonant frequencies.

Contextual Notes

The original poster notes a potential typo in their earlier message and reflects on the textbook's answers, which may imply a need for further verification of the calculations. The problem context is framed within the constraints of a homework assignment, which may limit the depth of exploration allowed.

qszwdxefc
Messages
10
Reaction score
0

Homework Statement



A closed air column is 60.0cm long. Calculate the frequency of the forks that will cause resonance at:

a) the first resonant length
b) the second resonant length

Note that the speed of sound is 344m/s.

Homework Equations



Ln = (2n - 1) * \lambda / 4

fn = (2n - 1)f1, where f1 = V/4L and 4L = \lambda

The Attempt at a Solution



I cannot figure out what the actual magnitude of the resonant length is, and don't know how to begin solving the problem.

Thanks.
 
Physics news on Phys.org
On the back of the page, the question additionally asks for the third resonant length.

The textbook provides answers for a, b, and c as 143Hz, 430Hz, and 770Hz respectively. When I reversed the calculations for c), they used a third resonant length of 60.0cm, which was the length of the whole air column.

I still can't figure out how they got the answers for a and b though :S.
 
qszwdxefc said:
On the back of the page, the question additionally asks for the third resonant length.

The textbook provides answers for a, b, and c as 143Hz, 430Hz, and 770Hz respectively. When I reversed the calculations for c), they used a third resonant length of 60.0cm, which was the length of the whole air column.

I still can't figure out how they got the answers for a and b though :S.

Perhaps I misled with my typo, though you wrote it correctly

But to state your equations again:
f1 = v/(4L)
fn = (2n - 1)*f1

4*L = 4*.6 = 2.4

f1 = 343/2.4 = 143

f2 = 3*f1

f3 = 5*f1
 
Makes sense, I understand now.

Thanks again :).
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
3K
Replies
3
Views
4K
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
3
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 12 ·
Replies
12
Views
13K
Replies
3
Views
7K
  • · Replies 3 ·
Replies
3
Views
3K