Calculating Speed of Sound in Air: Using Graphs and Harmonics

[benedwards2020]

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

 

[nrqed]

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).

 

[benedwards2020]

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)

 

[nrqed]

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.

 

[benedwards2020]

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?

 

[nrqed]

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 hav ebeen generating higher harmonics.

The general formula is

v = 2 L f /n

 

[benedwards2020]

Ok... But isn't that formula the same as I suggested in my original post? (assuming the 1st harmonic?)

 

[nrqed]

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.