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AUD202 Audio and Acoustics Theory. The Decibel Inverse Square Law / SPL Meters. Last Week >. The Human Ear and the Hearing Process Noise Induced Hearing Loss Hearing Protection OH&S Principles. UPCOMING REPORT!!!. Noise Induced Hearing Loss Report. 1000 words

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The Decibel Inverse Square Law / SPL Meters

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Audio and Acoustics Theory

The Decibel

Inverse Square Law / SPL Meters

Last Week >

The Human Ear and the Hearing Process

Noise Induced Hearing Loss

Hearing Protection

OH&S Principles


Noise Induced Hearing Loss Report

1000 words

Requires Reference and Bibliography Sections

Lots of things to follow in the JMC Style Guide

Upcoming Events

18 Days - NIHL Report

39 Days - Sound Observations Report

49 Days - Exam


The Decibel is a logarithmic value that expresses the ratio between two quantities.


White noise -3dB per step

White noise -1dB per step


White noise -0.3dB per step


Logarithms are useful because we can conveniently represent very large or small numbers, and carry out multiplication of ratios by simple addition and subtraction.

Some examples:

1000 watts relative to 1 watt is 30dB

100,000 watts relative to 1 watt is 50dB

100,000,000 watts relative to 1 watt is 80dB


The logarithm of a number is the power which the base has to be raised to produce that number

The logarithm of 1000 is 3, because 1000 is base 10 to the power 3

1000 = 10³ = 10 x 10 x 10

Calculating a Difference in dB

The difference in dB between 100 and 1

100 / 1 = 100

Log100 = 2

Log100 = 2 Bells

The decibel is 1 tenth of a Bell, so:

2 Bells x 10 = 20 Decibels

0dB Reference Values

0dBSPL= 0.00002 Pa

0dBV = 1 Volt

0dBu= 0.775 Volts

0dBm= 0.001 Watts

The dB Formulas

Sound Pressure Levels

dBSPL = 20 x log (SPL / SPLref)


dBV = 20 x log (V / Vref)

dBu = 20 x log (V / Vref)


dBm = 10 x log (P / Pref)

Sound Pressure Level (SPL)

Sound Pressure Level is a logarithmic measure of the sound pressure relative to a reference level

0dBSPL = 0.00002 Pa (20 µPa)

dBSPL = 20log (SPL / SPLref)

SPL is the measured sound pressure (in cm²)

SPLref is the reference sound pressure (0.00002 Pa)

Voltage (V)

Voltage is the potential difference between two points (e.g. the + and - sides of a battery)

0dBV = 1 volt

dBV = 20log (V / Vref)

V is the measured voltage

Vref is the reference voltage (1 volts)

Voltage (u)

dBu is referenced to 0.775 volts RMS (Root Mean Square)

0dBu = 0.775 volts

dBu = 20log (V / Vref)

V is the measured voltage

Vref is the reference voltage (0.775 volts)

Power (P)

Power is the rate at which energy is produced or used

0dBm = 0.001 watts

dBm = 10log (P / Pref)

dBm is the signal level

P is the measured wattage

Pref is the reference wattage (0.001 watt)

Two Line Level Standards

Pro equipment:


Consumer equipment:


+4dBu and -10dBV

Pro equipment signal level is +4dBu

Consumer equipment signal level is -10dBV

0dBu = 0.775 volts

0dBV = 1 volt


Sound Pressure Level (SPL) is measured in Pascals (Pa) and 0dBSPL is 0.00002Pa

Sound Intensity Level (SIL) is measured in watts per square meter (W/m2). 0dBSIL is: 10-12W/m2 or 0.000000000001W/m2


Sound Intensity (SIL) is difficult to measure which is why we typically use Sound Pressure (SPL).

RMS vs Peak

  • The peak value is the highest voltage that the waveform reaches

  • The RMS (Root-Mean-Square) value is the effective value of the total waveform. In audio it is the continuous or music power that the amplifier can deliver.

  • The effective or rms value of a sine wave of current is 0.707 times the maximum value of current 

RMS vs Peak Voltage


SPL Meters

In order to measure sound levels we need a calibrated microphone, preamp and display.

We have various settings to allow us to choose what we’re measuring (such as transient response & frequency response).

Digitech SPL MeterModel: QM 1589

Bruel & Kjaer 2250 Sound Level Meter

SPLnFFT Noise Meter By Fabien Lefebvre

SPL Graph by Studio Six Digital.

“SPL Graph is an audio level chart recorder for the iPhone… You can optionally record the audio for the graph, and even email graph results at the end of a test” (Studio Six Digital 2013).

Weighted Frequency Responses

Fig.1 A-Weighted frequency response

(, 2014)

Fig.2 A-Weighted frequency response

(, 2014)

SPL Meters

The options to understand on an SPL meter are:

  • A-weighting versus C-weighting

  • Fast or slow response

  • High or low (volume range)

    Remember, the A-weighting is close to human perception of loudness


The Inverse Square Law

In a free field, doubling the distance from the source results in a level drop of approximately 6 dB

The Inverse Square Law

Next Week >

The Doppler Effect

Delay Perception

SPL Meters


  • Institute of Acoustics >

References, (2014). Frequency Weightings - A-Weighted, C-weighted or Z-Weighted. [online] Available at: [Accessed 10 May 2014]

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