The Decibel Inverse Square Law / SPL Meters

The DecibelInverse Square Law / SPL Meters

AUD202Audio and Acoustics Theory

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THE DECIBEL

The Decibel is a logarithmic value that expresses the ratio

between two quantities.

Decibel

White noise -3dB per step

White noise -1dB per step

http://www.phys.unsw.edu.au/jw/dBNoFlash.html

Decibel

White noise -0.3dB per step

http://www.phys.unsw.edu.au/jw/dBNoFlash.html

Logarithms

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 30dB100,000 watts relative to 1 watt is 50dB100,000,000 watts relative to 1 watt is 80dB

Logarithms

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 = 100Log100 = 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 LevelsdBSPL = 20 x log (SPL / SPLref)

VoltagedBV = 20 x log (V / Vref) dBu = 20 x log (V / Vref)

WattsdBm = 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 voltageVref 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 voltageVref 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 levelP is the measured wattagePref is the reference wattage (0.001 watt)

Two Line Level Standards

Pro equipment: +4dBu

Consumer equipment: -10dBV

+4dBu and -10dBV

Pro equipment signal level is +4dBuConsumer equipment signal level is -10dBV

0dBu = 0.775 volts0dBV = 1 volt

SPL and SIL

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

SPL and SIL

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

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).

Fig.1 A-Weighted frequency response (Au.noisemeters.com, 2014)

Fig.2 A-Weighted frequency response (Au.noisemeters.com, 2014)

Weighted Frequency Responses

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

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 EffectDelay Perception

SPL Meters

Links

• Institute of Acoustics > ioa.org.uk

ReferencesAu.noisemeters.com, (2014). Frequency Weightings - A-Weighted, C-weighted or Z-Weighted. [online] Available at: http://au.noisemeters.com/help/faq/frequency-weighting.asp [Accessed 10 May 2014]