The decibel (abbreviated as ‘dB’) seems to be everywhere in the world of NVH measurements. It may seem like a unit of measurement (as it is typically shown on the Y-axis) but really it’s not, it is unit-less. We see it used in acoustics, vibration, electronics, telephony, audio engineering & design…. But what is this unitless-unit, why is it used, and how do we use it correctly?
This article has the following contents: 1. Background 2. Formulation 3. Reference for Acoustics 4. Simcenter Testlab Example 5. Double Check - Simcenter Testlab Units Editor
The decibel was originally developed and used by the telephone industry to quantify power loss in telegraph and telephone signals when sent through long cables. It is named in honor of Alexander Graham Bell, a pioneer in the field of telecommunication. While a decibel is defined as one tenth of a Bel, the Bel unit is rarely used.
The decibel is not a traditional unit of measure - it is a logarithmic ratio between two numbers. By using decibels, it can be easier to compare different values. Take the sound scale shown in pressure in Figure 1:
Figure 1: Pressure scale of sound has a wide range of numbers ranging from many zeros after the decimal place to whole numbers.
The numbers in the sound pressure scale range from very small (many digits after the decimal) to whole numbers.
Now consider the same numerical values expressed in decibels as shown in Figure 2:
Figure 2: Decibel scale of same pressure numbers.
The values are easier to compare. They are all whole numbers and "closer" in magnitude.
The next section explains how numbers (like the pressure values) are converted to decibels.
The decibel is a logarithmic ratio between two numbers – a measured value and a reference value. It is shown in two forms below: Equation 1 for POWER quantities , and Equation 2 for field AMPLITUDE quantities.
Equation 1: Examples of POWER quantities: Sound Power (Watts), Sound Intensity (Watt/m2), electrical Power, electrical Intensity, etc.
Equation 2: Examples of AMPLITUDE quantities: Pressure (Pa), Voltage (V), Acceleration (m/s2), temperature, etc.
As the decibel value depends entirely on the ratio between a measured value and the reference value, it is therefore critical to select the proper reference for the calculation. This is particularly important when comparing values between tests or measurements.
In acoustics, dB are often used to report sound pressure level (SPL). The reference for pressure in Pascals has been established as 20 micro Pascals (20e-6 Pa) as shown in Figure 3.
Figure 3: Reference value sound pressure (20 micro Pascals or 20e-6 Pa) is based on the threshold of hearing at 1000 Hz.
This value represents the average human hearing threshold at 1000 Hz, or the smallest pressure fluctuation perceivable to the average human ear at 1000 Hz.
Let’s take a look at a sample calculation to see how it works.
4. Simcenter Testlab Example
Using Simcenter SCADAS hardware and Simcenter Testlab (formerly called LMS Test.Lab) software, suppose you set up a microphone to record an orchestra. While they are tuning their instruments you make a quick recording. The RMS amplitude of the sound reads 1.084 Pascals. What is the dB amplitude of the sound shown in Figure 4?
Figure 4: Frequency spectrum of recording shown in Amplitude format.
Since sound pressure is an AMPLITUDE quantity, we will use the formulation below
Remember our dB Reference for Sound Pressure Level is 20 micro Pascals. Filling in our equation we get the following:
You can check your work by having a Simcenter Testlab display your recording in decibel format.
Right-click on the Y-axis, select “Format”.
Then select “dB/Level”.
The cursor now reads in decibels as shown in Figure 5:
Figure 5: After right clicking on the Y-axis and selecting "Format -> dB/Level" the cursor reads 94.78 dB.
Looks like we got the correct answer! Of course this is ONLY because we chose the same reference value as Simcenter Testlab used.
5. Double Check - Simcenter Testlab Units Editor
The default reference value that Simcenter Testlab (formerly called LMS Test.Lab) uses for any decibel calculation can be found by looking in the Configuration & Units System editor as shown in Figure 6.
Figure 6: The Simcenter Testlab units editor.
The reference values for other quantities like acceleration will be different than the reference values for sound pressure. Changing the reference changes the corresponding decibel value.