# Acoustic Standing Waves

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# 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 1458 millimiters long PVC tube (sometimes referred to as "Kundt's tube"). On one end there is a fixed speaker that can produce an audio sine, a triangular or a single pulse wave. On the opposite side there is a movable piston, changing the effective length 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 (membrane of the speaker )

The reference mic (Mic 1) should be used to verify that the emitted sound is the desired one (i.e., there is no distortion caused by the speaker). On the piston surface there is another microphone (Mic 4) capable of moving between 1269mm and 1475mm. The sound is acquired 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 of each 200ms sample. These values should be thoroughly analysed because of the non-liniarity in frequency of the speaker(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 intensity (constructive interference). The membrane of the speaker, as opposed to what might be sugested by common sense, does not "close" the tube. This happens because the membrane oscillates with the air (in the same way that a person pushing a swing is not considered an obstacle). This type of interference 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 phenomenon at hand. The following table shows some typical values of the experiment:

Table 2 – Typical experimental values
Harmony Frequency (Hz)
with piston at 1.45m
Resonance 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 (the piston is always an anti-node pressure when in ressonance).

However, there are some parts of the tube, called nodes, where the amplitude is zero (or close to zero). An interesting challenge 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. determine 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 resonance condition is different but, because there is partial reflection on the piston, it is harder to interpret.