Rearrange formula to show a linear relationship between Frequency and Volume

Click For Summary

Homework Help Overview

The discussion revolves around rearranging a formula relating frequency and volume in a physical context, specifically examining the equation $$ f=\frac{cs}{2\pi}\cdot\sqrt{\frac{A}{VL}} $$ to establish a linear relationship. Participants are exploring how to linearize this equation for graphical representation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss squaring the equation to facilitate linearization, questioning how to express frequency as a function of volume. There are inquiries about the definitions and relationships of the variables involved, such as speed of sound, area, and length.

Discussion Status

Several participants have provided steps and suggestions for rearranging the equation, including the possibility of using logarithmic scales for plotting. There is an ongoing exploration of different methods to achieve a linear representation, with some participants expressing skepticism about the necessity of logarithmic transformations.

Contextual Notes

Participants are clarifying the roles of constants and variables in the equation, with specific emphasis on the independence of certain variables and the nature of the experimental setup. The discussion reflects a mix of theoretical and practical considerations in the context of data analysis and graphing.

  • #31
Chestermiller said:
please provide the f vs V data, and I will show you what I mean. Plus, I have already answered these questions in a previous post.
V= 0,000295m^3 f=172Hz
V= 0,000245m^3. f=188Hz
V=0,000195m^3 f=211Hz
V= 0,000145m^3 f=245Hz
V=0,000095m^3 f= 303 Hz
V=0,000045m^3 f= 440Hz
 
Physics news on Phys.org
  • #32
qq194 said:
V= 0,000295m^3 f=172Hz
V= 0,000245m^3. f=188Hz
V=0,000195m^3 f=211Hz
V= 0,000145m^3 f=245Hz
V=0,000095m^3 f= 303 Hz
V=0,000045m^3 f= 440Hz
1692448410720.png
 
  • #33
Chestermiller said:
now it works, thank you , with me the graph looked like a straight line, only my associated function equation y=mx+b was not as perfect as yours. Many thanks, what program did you use?
 
  • #34
qq194 said:
now it works, thank you , with me the graph looked like a straight line, only my associated function equation y=mx+b was not as perfect as yours. Many thanks, what program did you use?
Kaleidagraph
 
  • #35
Chestermiller said:
Kaleidagraph
Chestermiller said:
Chestermiller said:
Kaleidagraph
thank you so much for your really great support!
 
  • #36
kuruman said:
"f" is frequency "V" is some kind of volume and ##c_s## is the speed of sound. By dimensional analysis, ##A## and ##L## are, respectively, some kind of area and length. I know all this because initially OP attached a pdf which was since deleted. There was no information on the physical situation in the pdf.
thanks for your help!
 
  • #37
Chestermiller said:
so that's the last question, how can I determine cs from this function equation between f and v now?because $$ y=kx^n $$
that describes only f and V in the diagram, can I determine cs with the help of these straight lines?
 
  • #38
qq194 said:
so that's the last question, how can I determine cs from this function equation between f and v now?because $$ y=kx^n $$
that describes only f and V in the diagram, can I determine cs with the help of these straight lines?
$$k=\frac{c_s}{2\pi}\sqrt{A/L}$$
 
  • Like
Likes   Reactions: qq194

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
936
  • · Replies 11 ·
Replies
11
Views
1K
Replies
3
Views
806
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
925
Replies
17
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
28
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K