• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11

# 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

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.

Middle

65

50

66

60

66

70

67

80

69

100

73

120

74

140

75

160

76

180

77

200

77

220

78

240

79

260

83

280

84

300

84

320

84

340

84

360

84.5

380

85

400

85

420

85

440

85.5

460

86

480

86

500

86

540

86.5

580

87

620

87

660

88

700

88

740

88

780

89

800

90

Figure 7

These results were then plotted.

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.

Figure 9

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

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.

This student written piece of work is one of many that can be found in our GCSE Waves section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Waves essays

1. ## Is Sunbathing Good?

4 star(s)

Pg3 UV and your health... Using sun beds can be safe if you follow certain rules that are given with the machine. One example of this is a Instruction book that comes with a Phillip sun bed. UV sessions: You may have one UV session per day, over a period of five to ten days.

2. ## is sunbathing good for you?

Many people become addicted to tanning, which is unofficially known as Tanorexia. Some of the symptoms of Tanorexia include a false belief that he or she is too pale, and will therefore exceed the limits of UV exposure. The individual will seek out UV exposure indoors or outdoors, with the

1. ## The aim of my experiment is to see what factors affect electromagnetism the most ...

As the number of coils or the current increases so does the power of the electromagnet. Firstly because the wire has a current running through it, a current which hold electrons that creates a magnetic field, which can be concentrated into an iron core when wrapped around it in like a coil.

2. ## Is the speed of sound affected when it travels threw different temperatures of air

was down to the a fall temperature because the tempreture was not being very carefully When a tuning fork is held over a tube, a standing wave pattern is formed in the tube. UndeSelected Sound Speeds in Gases Gas Temperature (�C)

1. ## Physics Case Study - Do Sunbeds Cause Skin Cancer?

Everybody's skin contains melanin, that's what gives our skin it's colour, it is produced by cells called melanocytes, which send the pink pigment up through the epidermis, where it is absorbed by other skin cells. The amount of melanocytes in our bodies is constant, everybody has around 5 million, however, genes dictate how much melanin your melanocytes produce.

2. ## Investigating the Relationship Between Real and Apparent Depth.

of the glass block, to determine the apparent depth I simply found the place where the drawing pin lined up with the optical pin even when I moved my head form side to side. The real depth was the distance from the optical pin to the drawing pin.

1. ## Soil water content in relation to species diversity in a Pingoe.

The main reason is grazing, young and less resilient plants will also be subject to trampling from large animas such as the cattle found at Fouldon common, this may cause an abundance of more hardy plants such as grasses. The excretion of nitrogenous waste from the animals in the area will act as a natural fertiliser to the surrounding vegetation.

2. ## Light is so common that we often take it for granted.

We see all other things because light from a source bounces off them and travels to us. Light sources can be classified as natural or artificial. Natural light comes from sources that we do not control. Such sources include the sun and the stars.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to