Calculating Speed of Sound in Air: Using Graphs and Harmonics

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Homework Help Overview

The discussion revolves around calculating the speed of sound in air using resonance experiments and graphical analysis. Participants explore the relationship between frequency and length in the context of sound waves in a tube.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss plotting frequency against length and the implications of such a graph. There is a suggestion to plot frequency against the inverse of length instead, with questions about the linearity of the resulting graph. Some participants express uncertainty about the experimental setup and the nature of the harmonics involved.

Discussion Status

The conversation is ongoing, with participants sharing insights about the graphical representation of the data and the relationship between frequency and length. Some guidance has been offered regarding the correct plotting method and the importance of understanding the harmonic being excited. There is recognition of the need for clarity on the assumptions made in the experiment.

Contextual Notes

Participants note constraints such as the inability to recreate the experiment and the need for clarity on the harmonic modes being considered. There is also mention of the potential for confusion if higher harmonics are inadvertently excited during the experiment.

benedwards2020
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Can someone tell me how I find the speed of sound in air?

If I plot a graph of frequency against length would I be right in saying that I can find the speed of sound by finding where the two points on the graph intersect and multiplying by 2, so that

v = 2 * Lf
 
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benedwards2020 said:
Can someone tell me how I find the speed of sound in air?

If I plot a graph of frequency against length would I be right in saying that I can find the speed of sound by finding where the two points on the graph intersect and multiplying by 2, so that

v = 2 * Lf

What do you mean by "where the two points intersect"?? I am not sure what that means.

Note that if you plot f versus L, you will not get a straight line at all. But if you plot f versus one over L, then you will get a straight line and the slope will be equal to v/2. So speed = twice the slope of a f versus 1/L graph. This is clear from f = V/(2L).
 
What I'm trying to do is to find the speed of sound in air. I have the resonance experiment in mind where a frequency is applied to a tube of air and measurements taken of the length of the tube where resonance occurs for that particular frequency.

So what you are saying is that I should plot the frequency against 1/L? is that correct? I'm not sure I understand why I wouldn't get a straight line graph if I plotted frequency against length. (I can't recreate the experiment to find out for myself)
 
benedwards2020 said:
What I'm trying to do is to find the speed of sound in air. I have the resonance experiment in mind where a frequency is applied to a tube of air and measurements taken of the length of the tube where resonance occurs for that particular frequency.

So what you are saying is that I should plot the frequency against 1/L? is that correct? I'm not sure I understand why I wouldn't get a straight line graph if I plotted frequency against length. (I can't recreate the experiment to find out for myself)

I am assuming that you are varying the length and measure the fundamental frequency of the tube as a function of the length (not of excited modes), right?

You can see from the formula that f = v/(2L)

If you call f = y and L = x, you get y = c/x with c = V/2 .
If you plot a function y =c/x you don'tget a staright line since it's not of the form y = mx + b.
 
I want to excite the tube with a range of frequencies, and record the length where resonance occurs

I think I see what you mean about the graph not being a straight line... It needs to be in the right form...


Is there a list of similar results I could take a look at somewhere? I think I need to see for myself what is going on?
 
benedwards2020 said:
I want to excite the tube with a range of frequencies, and record the length where resonance occurs
I understand. The only tricky thing is to know what harmonic you are exciting. The formula you gave is only valid for the fundamental mode of a pipe open at both ends.

I think I see what you mean about the graph not being a straight line... It needs to be in the right form...


Is there a list of similar results I could take a look at somewhere? I think I need to see for myself what is going on?
I am sure that a google search would give some results. But it's pretty straightforward...just plot your points and you will get a straight line. If you get a straight line but the speed comes out to be way off, you might have ebeen generating higher harmonics.

The general formula is

v = 2 L f /n
 
Ok... But isn't that formula the same as I suggested in my original post? (assuming the 1st harmonic?)
 
benedwards2020 said:
Ok... But isn't that formula the same as I suggested in my original post? (assuming the 1st harmonic?)

Yes, it is. I simply gave it for any harmonic. Just in case that could be useful to you.
 

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