Rearrange formula to show a linear relationship between Frequency and Volume

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SUMMARY

The discussion focuses on rearranging the formula $$ f=\frac{c_s}{2\pi}\cdot\sqrt{\frac{A}{VL}} $$ to establish a linear relationship between frequency (f) and volume (V). Participants suggest squaring the equation to yield $$ f^2 = \left(\frac{c_s}{2\pi}\right)^2 \cdot \frac{A}{VL} $$, which can be plotted as $$ y=f^2 $$ against $$ x=\frac{1}{V} $$, resulting in a straight line with slope $$ m=\left(\frac{c_s}{2\pi}\right)^2 \frac{A}{L} $$. This approach eliminates the need for logarithmic transformations, simplifying the analysis.

PREREQUISITES
  • Understanding of basic algebra and manipulation of equations
  • Familiarity with the concepts of frequency and volume in physical systems
  • Knowledge of linear regression techniques for data analysis
  • Experience with plotting software for graphing data
NEXT STEPS
  • Research linear regression methods in Excel or LibreOffice for data analysis
  • Learn about the physical significance of the speed of sound ($$ c_s $$) in various media
  • Explore the implications of dimensional analysis in the context of frequency and volume
  • Investigate the use of plotting software for creating linear and log-log plots
USEFUL FOR

Students and professionals in physics, engineering, and data analysis who are interested in understanding the relationship between frequency and volume in experimental setups.

  • #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
 
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  • #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?
$$k=\frac{c_s}{2\pi}\sqrt{A/L}$$
 

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