Stationary Wave Lab: Exploring Antinodes, Length & Frequency

[Vey2000]

The lab experiment involved stationary sound waves within an open tube produced by a speaker placed near one of the ends of the tube.
There are three questions I am unsure of.
a) The antinodes near the ends of the tube are not located exactly where the tube ends. Why is this?
b) Estimate from the data the effective length of the tube.
c) Does the effective length depend on the frequency?
Question a doesn't bother me too much actually. Haven't covered waves (in a more advanced sense, I suppose) yet this year, but we did study waves a bit last year in the intro physics course. If I remember correctly, the professor explained that this occurs because the antinode isn't fixed to where the tube ends, or something like that.
For part b (and c also) I've proceeded in the following manner, but I'm not sure if I'm correct.
The first ten harmonic modes were located and the corresponding frequency measured. Through a least squares regression (f(n)=v*n/(2L)) the speed of sound was calculated. (This was required for the lab report.)
Then using the same equation and the speed of sound I obtained I calculated L for each mode. Indeed, the values of effective L differ from L0, within about 1 cm of it. Actually, they're still technically within the error I calculated for them. L0 is approximately 60 cm, just to give a sense of proportion.
The values of the effective L don't seem to be linear with mode either. Perhaps amplitude affects it, since we did change the amplitude between frequencies to keep it within the range of the oscilloscope (and make it bearable on the hearing)
Frankly, I don't think this is the correct way to measure the effective length. Most likely I simply calculated the original length for subsets of the data, which is why they're slightly different yet still mostly within the bounds of the error.

 

[Jhero]

Hello! Thank you for sharing your thoughts and calculations on this lab experiment. It seems like you have a good understanding of the concept of antinodes and the effect of amplitude on the location of these antinodes.

For question a, you are correct in thinking that the antinodes are not located exactly where the tube ends because they are not fixed to the ends of the tube. In fact, antinodes can occur at any point along the length of the tube, depending on the frequency and amplitude of the sound waves. This is because the sound waves are reflected at the ends of the tube and interfere with each other, creating nodes and antinodes.

For part b, it seems like you have used the correct equation to calculate the effective length (L) of the tube. However, it is important to note that the effective length may vary slightly due to experimental errors and variations in the amplitude of the sound waves. It is also possible that the effective length is not exactly linear with the mode, as you have observed. This could be due to the effects of amplitude or other factors such as the shape and diameter of the tube.

For part c, the effective length does indeed depend on the frequency. As the frequency increases, the distance between nodes and antinodes decreases, resulting in a shorter effective length. This can be seen in your calculations, where the effective length is slightly shorter for higher frequency modes.

Overall, it seems like you have a good understanding of the concepts and have approached the calculations correctly. However, it is always important to consider experimental errors and other factors that may affect the results. Keep up the good work!