Acoustic Standing Waves
Description of the Experiment
The purpose of this experiment is to explore basic concepts of stacionary waves, using sound.
Experimental Apparatus
The apparatus is a PVC tube (sometimes refered to as "Kundt's tube"), with 1458 millimiters in length. On one end there is a fixed speaker that can produce an audio sine, triangular or a single pulse wave. On the opposite side there is a movable piston, changing the effective lenght of the tube. Along the tube there are several microphones to register the sound intensity at fixed points.
The following table shows the positions of the microphones in relation to the source (speaker):
| Designation | Distance to source (mm) |
|---|---|
| Mic 1 (reference) | 250 |
| Mic 2 (center) | 750 |
| Mic 3 (extremity) | 1250 |
| Mic 4 (embolus surface) | Entre 1260 e 1480 |
| Extremidade do tubo | 1450 |
The reference mic (Mic 1) should be used to verify that the emitted sound is the disered on (i.e., there is no distortion caused by the speaker). On the piston surface is another microphone (Mic 4) capable of moving between 1269mm and 1475mm.
The sound is aqquired through 2 channels of a sound card: the left channel (CH 1) is always bounded to the reference microphone (Mic 1); the other channel (CH 2) can be connected to one of the other three microphones.
The experimental data is captured by the soundcard and processed online (normalization).
Protocol
This assembly is also used for the stationary wave experiment, and thus has two modes of operation: in "Stationary" mode (position and frequency sweep), the rms value of the soundwave is registered in power decibels. This is done by averaging the tms amplitude for 200ms each sample. These values should be thoroughly analysed because of the speaker's non-liniarity in frequency (this can lead to a wrong interpretation of results).
The ststionary waves occur when the length of the tube is a multiple of half the wavelength.
\[ L = n \times \frac{\lambda}{2} = n \times \frac{v_{som}}{2 \times f} \quad n=1,2,3,... \]
However, if one of the ends is open (speaker) and the other is closed (piston) the condition changes to:
\[ L = (2n-1) \times \frac{v_{som}}{4 \times f} \quad n=1,2,3,... \]
[...]
| Harmony | Frequency (Hz) with piston at 1.45m |
Ressonance distance (m) with frequency at 740Hz |
|---|---|---|
| 1 | 117.24 | 0.23 |
| 2 | 234.48 | 0.46 |
| 3 | 351.72 | 0.69 |
| 4 | 468.97 | 0.92 |
| 5 | 586.21 | 1.15 |
| 6 | 703.45 | 1.38 |
| 7 | 820.69 | 1.61 |
| 8 | 937.93 | 1.84 |
| 9 | 1055.17 | 2.07 |
| 10 | 1172.41 | 2.30 |
