Determination of the Speed of Sound

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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:

\[ v_{sound} = \frac{\Delta s}{\Delta t} \] 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