Difference between revisions of "Acoustic Standing Waves"

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The experimental data is captured by the soundcard and processed online (normalization).
 
The experimental data is captured by the soundcard and processed online (normalization).
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=Protocol=
 
=Protocol=

Revision as of 11:14, 21 April 2013

Description of the Experiment

The purpose of this experiment is to explore basic concepts of standing waves, using sound.


Links

  • Video: rtsp://elabmc.ist.utl.pt:554/statsound.sdp
  • Laboratory: Advanced in e-lab.ist.eu[1]
  • Control room: statsound
  • Level: ****


<swf height="290" width="500">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/StatSound.swf</swf>


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) 36
Mic 2 (center) 746
Mic 3 (extremity) 1246
Mic 4 (embolus surface) between 1269 and 1475
Tube's extremity 1455
Table 1 – Microphones distance to the sond source (speaker's membrane)


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 "Standing" 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 standing waves occur when the length of the tube is a multiple of half the wavelength.

\[ L = n \times \frac{\lambda}{2} = n \times \frac{v_{sound}}{2 \times f} \quad n=1,2,3,... \]

However, if one of the ends is open (speaker) and the other is closed (piston) the condition changes to:

\[ L = (2n-1) \times \frac{v_{sound}}{4 \times f} \quad n=1,2,3,... \]

In this case, the wave reflected by the piston reaches the speaker just as another wave is being generated (same phase), so there is a high increase in the sound's intensity (constructive interferance). The speaker's membrane, as opposed to what might be sugested by common sense, does not "close" the tube. This happens beacause de membrane oscillates with the air (in the same way a person pushing a swing is not considered an obstacle). This type of interferance occurs when a plane exceeds the speed of sound, creating shock-waves.

In this situation, the intensity recorded by the microphones is very high and allows a clear view of the phenomenom at hand. The following table shows some tipical values of the experiment:

Table 2 – Tipical experimental values
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

Advanced Protocol

There are several experiments that can be done, like trying to understand why the insensity changes between microphones. To be precise, the standing wave is a sum of several waves that travel in opposing directions but have the same phase, which causes the intensity to be high in the anti-nodes (piston is always a pressure anti-node when in ressonance).

However, there are some parts of the tube, called nodes, where the amplitude is zero (or close to zero). An interesting chalenge is to calculate the position and frequency (of the piston and the wave, respectively) that create a node on one of the microphones and try to understand why there is still a reading or, alternatively, determine the maxima of the standing wave. The experiment can also be "reversed", i.e. deternime the frequency/distance relations that make the wave null, which means a destructive interferance between reflected and emitted waves.

A phenomenon that also occurs is the existence of standing waves with an open tube (position at 1450mm - piston on the outside). In this case, the sound wave finds an infinite at the tube's exit where the pressure is constant and thus behaves as a pressure node for the standing wave. Here, the condition for resonance is different but, because there is partial reflection on the piston, it is harder to interpret.


Links