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Investigate the relationship between sound pressure level (SPL) and signal amplitude.

Extracts from this document...

Introduction

Joe Benn 13:2                   A Level Physics – ‘Sound Level & Power’                       14/11/02

Sound Pressure Level & Amplitude

Aim

Investigate the relationship between sound pressure level (SPL) and signal amplitude.

Summery

I constructed the apparatus as shown below and collected results.  The results do not show what I expected and do not adhere to the rules and physical theory I have researched.

The investigation has not shown what I had intended it to but I can suggest several reasons as to why.

NB: Large copies of all the graphs used are included at the end of the document

Planning

As a sound engineer I have wondered for some time as to the relationship between increases in power output of a sound system and changes in sound pressure level (SPL).  It seems to me that there is not a direct relationship between the two.

I plan to simplify the idea of a sound system into a signal generator/amplifier and a single speaker.  The SPL will be measured using a sound pressure level meter (Figure 2).

Variables and constants; the SPL meter will be placed a fixed distance away from the speaker, the frequency emitted from the speaker with remain constant, the amplitude of the signal will be varied to change the power  output of the speaker.

Figure 1

image00.jpg

Figure 2

SPL meter as it was used in the application

I performed some preliminary experiments to determine:

  • The distance between the SPL meter and the speaker.
  • The frequency of the signal the speaker should emit.
  • The lowest amplitude that could be sensed by the SPL meter.
  • The highest amplitude that could be produced by the signal amplifier.

I found:

  • For the SPL meter to register at low amplitudes the furthest distance the speaker can be from the sensor is 3.5cm.
  • If the SPL meter is closer to than 2.5cm from the speaker the speaker driver causes interference and abnormally low SPL readings.
  • Due to the design of the speaker I was using, unusual buzzes and hums were audible at frequencies between 200 – 400Hz and 600 – 700Hz.  In order that these frequency problems do not cause anomalies in my results, the speaker will emit a constant 500Hz signal.
  • Signals with amplitude less than 10mV are not detectable at a distance of 3.5cm with the SPL meter I was using.
  • The signal amplifier I was using could produce a signal with amplitude of up to 800mV.
  • The scale on the amplitude control of the signal amplifier was inaccurate; to ensure accurate results I used an oscilloscope (CRT) to guarantee correct amplitudes.
  • The display on the SPL meter was small and difficult to read, to ensure accurate readings I connected the output terminals to a voltmeter with a Vu dial.
...read more.

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Figure 7

These results were then plotted.

image10.png

Figure 8

This graph shows a greater range of signal amplitudes, a logarithmic curve has been placed over the results and it fits very well, some of the points are not actually on the trend line but shape is very similar.

Intensity level is given by:

        L = log10(N/k)

        =>        L = log10(P/A/k)

        =>        L = log10(P/(Ak))

        since P=IV

        =>        L = log10[(IV)/(Ak)]

        and V=IR

        =>        L = log10[(V2/R)/(Ak)]

        =>        L = log10[V2/(RAk)]

        raise 10 to each side

        =>        10L = 10log10[V^2/(RAk)]

        since alogab = b

        =>        10L = V2/(RAk)

        Since R, A and k are constant, 10L is proportional to V2.

        VRMS is given by:

        VRMS = V x 0.50.5                [0.50.5 is root of a half]

        =>        10L = (VRMS/0.50.5)/(RAk)

        =>        10L = [(VRMS)2/0.5]/[RAk]

        =>        10L = 2(VRMS)2/(RAk)

        Where:

  • N = Intensity (in Wm-2)
  • L = Intensity Level (in dB)
  • k = Intensity at threshold of hearing, 1 pWm-2 (1x10^-12 Wm2)
  • P = Power (in W)
  • V = Maximum amplitude, aka Sound Pressure Variation (in V)
  • VRMS = Root mean squared amplitude, aka Effective Pressure    Variation (in V)

        Therefore, 10L should also be proportional to (VRMS)2.

To discern whether the results show this, a graph must be plotted; 10L against root mean squared amplitude2.

image11.png

Figure 9

The graph does not show a straight line as I would expect it to if they are proportional.

...read more.

Conclusion

In hindsight I should have realised the limitations of the SPL meter I was using much earlier in the investigation.  If I had, I could have changed the investigation so the SPL could be measured by the computer using one of the ‘LIVE’ boxes.  Using the computer could have brought about more accurate results because the scale available is much greater.  I decided not to use the computer to measure SPL because I could not make the meter sensitive enough to register the lower amplitudes.

I thought that I would have a great deal of problems with ‘background noise’, (any sound level which could be detected by the SPL meter which was not part of the investigation) however it was not as much of a problem as I had imagined.  The general background level in the lab was approximately 55dB for the duration of the investigation.  Very loud anomalous readings e.g. doors slamming could easily be ignored and the results recorded after this event.

Conclusion

I have succeeded in what I set out to do; I have taken results and proven that the relationship between SPL and amplitude is non-liner.  This said, I have not proven what I had expected to, the formulae I have included previously indicate what the results should be, and they are not.  The failure to prove the formulae correct are due to a number of reasons, as outlined above.

...read more.

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