The Decibel Inverse Square Law / SPL Meters AUD202 Audio 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

Decibel White noise -0.3dB per step

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 30dB 100,000 watts relative to 1 watt is 50dB 100,000,000 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 = 10 ³ = 10 x 10 x 10

Calculating a Difference in dB The difference in dB between 100 and / 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 0dB SPL = Pa 0dBV = 1 Volt 0dBu= Volts 0dB m = Watts

The dB Formulas Sound Pressure Levels dB SPL = 20 x log (SPL / SPLref) Voltage dB V = 20 x log (V / Vref) dB u = 20 x log (V / Vref) Watts dB m = 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 0dB SPL = Pa (20 µPa) dB SPL = 20log (SPL / SPL ref ) SPL is the measured sound pressure (in cm²) SPL ref is the reference sound pressure ( Pa)

Voltage (V) Voltage is the potential difference between two points (e.g. the + and - sides of a battery) 0dB V = 1 volt dB V = 20log (V / V ref ) V is the measured voltage V ref is the reference voltage (1 volts)

Voltage (u) dBu is referenced to volts RMS (Root Mean Square) 0dB u = volts dB u = 20log (V / V ref ) V is the measured voltage V ref is the reference voltage (0.775 volts)

Power (P) Power is the rate at which energy is produced or used 0dB m = watts dB m = 10log (P / P ref ) dB m is the signal level P is the measured wattage P ref 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 +4dBu Consumer equipment signal level is -10dBV 0dBu = volts 0dBV = 1 volt

SPL and SIL Sound Pressure Level (SPL) is measured in Pascals (Pa) and 0dBSPL is Pa Sound Intensity Level (SIL) is measured in watts per square meter (W/m 2 ). 0dBSIL is: W/m 2 or W/m 2

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 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 Meter Model: 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 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 Effect Delay Perception SPL Meters

Links Institute of Acoustics > ioa.org.uk

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