Follow the instructions from the guide sheet.

Please, read also the relevant pages from the Lab. Manual regarding the oscilloscope. The practice shows that this is the biggest challenge in the setup and data collection part of the Lab. Test.
Make sure you know how to make the connections and what are you supposed to monitor and measure.

In the guide sheet for the Lab.Test version of this experiment you are advised to take f   higher than 1000Hz.
As you may recall from the regular experiment, this means that you will have at least one full wavelength in the tube (you will not see the gravest mode, when the tube accommodates only half of the wavelength!)

In this experiment the frequencies used for measurements must all be RESONANCE frequencies! Make sure you know how to detect them. For example, keep the microphone as close to the speaker as possible, vary the frequency and observe the change in the amplitude of the signal displayed on the screen. At resonance you should see a sharp increase in the amplitude of the signal on the screen, as compared with the signal's amplitude at frequencies a bit lower and a bit higher than the resonance one.

Note:  Oddly enough, the experimental results show that even if you don't use the right frequencies (the resonance frequencies), the numerical value of the velocity you obtain is more or less the same with the one obtained with the correct method (and the resonance frequencies).
Nevertheless, it is important in principle that you use the correct method and the resonance frequencies.
Please, read again the (web-based) guide sheets for the regular experiment (Standing waves).

The reading errors

Once you get a resonance frequency try to see how precisely you can keep it.
To see this, move away from the f   you just found and try to catch the same resonance again; you'll see that your new f   is a bit off from the previous value. This gives you an estimate for the error in f.
Definitely, this "reading" error is larger than the (1/2 of the last digit) error, as naively one may quote the reading error (the usual argument is that the frequency is read on the digital display of the f -generator, and hence has a reading error of 1/2 of the last displayable digit - in our case 1Hz or 0.1Hz).

As for the reading error in the approach is the same.
Once you think you got a node, try to see how confident are you in its position.
Move the microphone a bit (left, right) and see by how much the image on the screen changes.
The practice shows that you may move the microphone by a few millimeters and see no change in the signal; therefore the uncertainty in the position of the microphone translates into a "reading" error for the distance between the nodes.
Accordingly, the reading error in the position of the node is NOT 0.2mm nor 0.3mm (both values underestimate the reading error), as one would naively take for the reading error (the usual argument is that you can see 1/5 or 1/3 of 1mm on the measuring tape).

Note 1:   Instead of looking for nodes you may choose to look for antinodes of the wave inside the tube.
In both cases the wavelength is twice the distance between successive nodes OR between successive antinodes.

Note 2:   To get   don't forget to multiply by 2 both the distance between successive nodes (which is /2 ) AND the reading error in it.

Note 3:  To avoid the hassle of multiplication (see above) you may count at once the distance between three successive nodes (or antinodes) and write down at once the  , with the corresponding reading error.

Example:
Assume you got the position of one node as x_L = (160.5 ± 0.2)cm, and of the 3rd node (skipping the one in between) as x_R = (183.7 ± 0.2)cm. Then,   is just the difference: = x_R - x_L = (23.2 ± 0.3)cm.

Graph

Choose the scale in such a way that the error bars are visible at least for one of the variables (usually, in the dependent one).
The relative error in is about 1% (or smaller), while the relative error in f  is about 0.2% or so.
Disclaimer: don't take my word for it - check your lab. notebook to see which are your values for the relative errors!
You may try to keep f  as your independent variable (on horizontal axis) and plot
(v  vs. f ), in which case the fit line will be a horizontal line (we expect that velocity doesn't depend on f ).
One last tip for this case: you have to "zoom in" the vertical (i.e. v ) axis if you want to be able to see the error bars (like in the Boyle's Law experiment, second graph of the regular experiment).

Alternatively, one may plot (   vs.   1/f ) in which case the fit line is tilted and its slope is v. 
Observe that for the independent variable I keep the one which has the smallest relative error - so that error bars are mainly vertical. This is not mandatory, but makes the plotting easier and the look of it more common.

Error calculus

Pay attention to error quotation in data.
In this particular experiment the reading errors in distance and frequency most probably require separate columns (they change with the trial). Make sure you have a neat and properly designed table. Don't forget the units!

(A):  If you choose to plot (v  vs. f ), then the fit lines should be horizontal.
Plotting (as in the Boyle's law experiment) the error bars in individual values of v  (I used "individual" to say that for each pair of and f you get a value for v) requires a bit of extra work, but at the end you may estimate the error in the mean value of v  much easier.
To get the error in the mean value of v  you have to shift your fit line up and down within the limits of error bars.

Note: getting the error bars in each value of v  is not as hard as you may think. In fact, the relative error in each value of v  is about the relative error in the corresponding , provided the relative error in f is as I said above, in the Graph section ( (0.2%)² is much smaller than (1%)²  ). Therefore, getting the error in each v it's very easy.

(B):  For the plot (   vs.   1/f ) the error in v  has to be retrieved using the minimum and maximum slope fit lines (see Lab. Manual, pp. 133-140 for details on fitting techniques).
One may expect to see error bars for but not for f.
Actually, while preparing for the Lab. Test you should convince yourself that this is the case, at least with the values you have in your lab. notebook. It might be that with your data (and at the Lab. Test) the outcome is different (although I don't expect to see that).

Conclusion

Make sure you quote the final result for velocity with the right units.
If you have an estimate for the error in v  be careful to quote it correctly - pay attention to the number of significant digits in the mean and the error.

 

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  Last revised: April 7, 2003
© Sorin Codoban, 2003