Rearrange formula to show a linear relationship between Frequency and Volume

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The discussion focuses on rearranging the formula f = (cs / 2π) * √(A / (VL)) to establish a linear relationship between frequency (f) and volume (V). By squaring both sides, the equation becomes f² = (cs² / (4π²)) * (A / (VL)), allowing for the identification of f² as the dependent variable and 1/V as the independent variable. This results in a linear relationship that can be plotted as f² versus 1/V, where the slope can be used to determine the speed of sound (cs). Participants emphasize that logarithmic transformations are unnecessary for this analysis, as the linear relationship can be effectively established through direct plotting. The derived equation successfully demonstrates the expected linear relationship, confirming its validity.
  • #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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