Difference between revisions of "Determination of the Speed of Sound"

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===Description of the Experiment===
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=Description of the Experiment=
 
The purpose of this experiment is to determine the speed of sound.
 
The purpose of this experiment is to determine the speed of sound.
  
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===Experimental Apparatus=== <!-- Secção colapsável -->
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'''Links'''
 
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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 speaker:
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*Video: rtsp://elabmc.ist.utl.pt:554/statsound.sdp
 +
*Laboratory: Advanced in e-lab.ist.eu[http://e-lab.ist.eu]
 +
*Control room: statsound
 +
*Level: ****
 +
 
 +
</div>
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</div>
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 +
 
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<swf height="290" width="500">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/StatSound.swf</swf>
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 +
 
 +
=Experimental Apparatus=
 +
The apparatus (sometimes referred as "Kundt's tube") consists of a 1458 mm lon PVC tube. On one end there is a fixed speaker that can produce an audio sine, triangular or single pulse wave. On the opposite side there is a movable piston to change the effective tube length. Along the tube there are several microphones to register the sound intensity at some fixed points.
 +
 
 +
The following table shows the positions of the microphones in relation to the source (speaker):
 +
 
 +
{| border="1"
 +
|-
 +
! Designation
 +
! Distance to source (mm)
 +
|-
 +
| Mic 1 (reference)       
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| 250
 +
|-
 +
| Mic 2 (center)   
 +
| 750
 +
|-
 +
| Mic 3 (extreme)
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| 1250
 +
|-
 +
| Mic 4 (embolus surface)
 +
| Between 1260 e 1480
 +
|-
 +
| tube limit
 +
| 1450
 +
|+ Table 1 – Microphones distance to the sound source (speaker's membrane)
 +
|}
  
Referência
 
Distância à fonte (altifalante)
 
Mic 1 (referência)
 
250 mm
 
Mic 2 (centro do tubo)
 
750 mm
 
Mic 3 (extremidade do tubo)
 
1250 mm
 
Mic 4 (superfície do êmbolo)
 
Entre 1260 e 1480 mm
 
Extremidade do tubo
 
1450 mm
 
Table 1 – Microphones distance to the sond source (speakers 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 reference mic (Mic 1) should be used to verify that the sound is emitted as desired (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 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 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).</div>
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The experimental data is captured by the PC's sound-card and processed on-line (normalization) before being received by the user.
</div>
 
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
  
===Protocol=== <!-- Secção colapsável -->
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=Protocol=
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This apparatus can also be used for the stationary wave experiment and thus has two modes of operation: in the "Speed of sound" mode the amplitude of the wave is registered over time.
This assembly is also used for the stationary wave experiment, and thus has two modes of operation: in the "Speed of sound" mode, the amplitude of the wave is registered over time.
 
  
To determine \( v_{sound} \), the user must choose a "pulse" type of stimullus and measure the "time-of-flight" taken by the wave from Mic 1 and any other microphone. The speed can be determined with data from table 1 and the formula for speed determination:
+
To determine \( v_{sound} \), the user must choose a "pulse" type of stimulus and measure the "time-of-flight" taken by the wave from Mic 1 and any other microphone. The speed can be determined with data from table 1 and the formula for speed determination:
  
\[
+
<math>
 
v_{sound} = \frac{\Delta s}{\Delta t}
 
v_{sound} = \frac{\Delta s}{\Delta t}
\]
+
</math>
 
where \(s\) is the distance between the selected microphones.
 
where \(s\) is the distance between the selected microphones.
Of course other waveforms could be used but a wise interpretations of phase as to be pursue.
+
Of course, other waveforms could be used but this would require a closer look at the signals phase.
</div>
 
</div>
 
 
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
 
 
===Advanced Protocol=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
Under construction.</div>
 
</div>
 
  
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===Data Analysis===
 
<div class="mw-collapsible-content">
 
Under construction.</div>
 
</div>
 
  
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=Advanced Protocol=
===Theoretical Principles=== <!-- Secção colapsável -->
+
Using the coherence function between the acquired signals, the phase determination can improve with higher accuracy among different microphones. Using an appropriate software package (like Matlab or Octave for instance) this phase is easily determined (mscohere). Pink or white noise are very suitable for this purpose as they won't show any phase indetermination.
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Under construction.</div>
 
</div>
 
  
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===Historical elements=== <!-- Secção colapsável -->
 
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Under construction.</div>
 
</div>
 
  
===Bibliography===
+
=Links=
Under construction.
+
*[[Determinação da Velocidade do Som | Portuguese Version (Versão em Português)]]

Latest revision as of 20:06, 24 May 2015

Description of the Experiment

The purpose of this experiment is to determine the speed of 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 (sometimes referred as "Kundt's tube") consists of a 1458 mm lon PVC tube. On one end there is a fixed speaker that can produce an audio sine, triangular or single pulse wave. On the opposite side there is a movable piston to change the effective tube length. Along the tube there are several microphones to register the sound intensity at some 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 (extreme) 1250
Mic 4 (embolus surface) Between 1260 e 1480
tube limit 1450
Table 1 – Microphones distance to the sound source (speaker's membrane)


The reference mic (Mic 1) should be used to verify that the sound is emitted as desired (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 PC's sound-card and processed on-line (normalization) before being received by the user.


Protocol

This apparatus can also be used for the stationary wave experiment and thus has two modes of operation: in the "Speed of sound" mode the amplitude of the wave is registered over time.

To determine \( v_{sound} \), the user must choose a "pulse" type of stimulus and measure the "time-of-flight" taken by the wave from Mic 1 and any other microphone. The speed can be determined with data from table 1 and the formula for speed determination:

[math] v_{sound} = \frac{\Delta s}{\Delta t} [/math] where \(s\) is the distance between the selected microphones. Of course, other waveforms could be used but this would require a closer look at the signals phase.


Advanced Protocol

Using the coherence function between the acquired signals, the phase determination can improve with higher accuracy among different microphones. Using an appropriate software package (like Matlab or Octave for instance) this phase is easily determined (mscohere). Pink or white noise are very suitable for this purpose as they won't show any phase indetermination.


Links