Noise monitoring & evaluation Study Module 2
Assessment details
Purpose
This subject covers the ability to site and set up basic ‘ground level’ meteorological equipment and collect and record reliable data. It also includes the ability to assess data quality, interpret significant data features and use the data to ensure the validity of air and noise monitoring measurements.
Instructions
◗ Read the theory section to understand the topic.
◗ Complete the Student Declaration below prior to starting.
◗ Attempt to answer the questions and perform any associated tasks.
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◗ When completed, submit task by email using rules found on last page.
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Details
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Class code / NME
Assessment name / SM2
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Total Marks Available / 34
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Weighting / This is one of six formative assessments and contributes 10% of the overall mark for this unit
Chapter 2 – Acoustic theory
This section outlines the science behind sound. For those of you that actually enjoy science, then this will be a somewhat basic introduction into one small part of the world of physics. To those of you who don’t like science much, this part will…is compulsory to learn!
The basic physics of sound
The keys to understanding the acoustics of sound or noise lies in understanding pressure, which is a topic that should be familiar to you from previous study, but, along with time and distance shall be briefly revisited here, as well as understanding the properties of a wave in general.
Types of waves and their formation
Pressure, such as with atmospheric pressure, is the quotient of force and area, where force is measured in unit Newton. So if you apply a force over an area, you create pressure, whose unit is the Pascal, Pa. Sounds are merely a repeating of this process, which results in a pressure wave, which when heard is called a sound wave (although there are pressure waves we cannot hear). The pressure (sound) wave travels in a direction over a distance (which is usually measured in meters, m) over a period of time, t, measured in seconds, s.
Pressure travels in waves. Pressure waves we can hear are called sound waves. A sound wave is a pressure wave and vice versa.
Sound is caused when fluctuations in air pressure give rise to pressure waves which travel through a medium such as the atmosphere (but the medium can be any material). As the waves travel they will interact in various ways with their surroundings which tends to complicate things drastically, luckily though it is possible to describe the behaviour of sound in simple, idealized situations, and to use these to a better understanding of how it all works in the real world.
Figure 2.1 – Generation of a wave, in this case described as the fluctuation of high and low pressure where the ‘0’ value for pressure is equal to that of the atmosphere (which is variable). Biel & Hanson
But what is a wave? We need to introduce some basic theory about sound waves and their behaviour. Figure 2.1 shows the mechanical process using a piston as a metaphor. Without an in-depth discussion on particle velocities and inertia, as the piston moves forward, the air next to the piston ‘compresses’, increasing the force applied over the area of the piston, and pressure increases (relative to the atmospheric pressure) in a process termed compression. When the piston starts reversing, there is a reduction in the force being applied and therefore a reduction in the pressure (relative to atmospheric) as the air particles are less dense, a process called rarefaction.
The overall result is a cycle of positive and negative pressure fluctuations, and if we were to graph this process after several cycles we would see a graph in the shape of a sine wave, as seen in Figure 2.1.
Wave behaviour
Figure 2.1 shows the formation of a ‘wave’, but there is more to it than this as there are two different types of wave (of interest to us); the longitudinal and the transverse.
A transverse wave moves ‘up-and-down’, such as with waves in water where the peak of the wave is ‘up’ and the trough of the wave is ‘down’. A longitudinal wave is the opposite of this, that is, ‘side-to-side’. The sine graph could imply that the pressure wave is moving up and down, or transverse, which is wrong as the sound wave is travelling ‘side-to-side” or longitudinally. This is difficult to draw, so it is fortunate that a textbook has done that for us in the figure below.
Figure 2.2 – Depiction of sound pressure wave as a longitudinal wave. From South.
Wave properties
A wave has a number of significant properties, all of which will be explored in this section. The basic attributes that we will consider are amplitude, wavelength, time, distance, frequency and the speed of sound (velocity, which most of the time we shall assume is constant).
For this to make sense, you need to constantly remind yourself that we are talking about waves of sound pressure, travelling through the air
Amplitude
With reference to sound pressure, amplitude (A) is simply how far a particle moves from the rest position when a wave passes, or more simply - the degree of pressure fluctuation. The greater the particle moves from the rest position the larger the sound wave and the greater the amount of energy that is carried by the wave.
If you have trouble with this concept think about the last time you were at the beach. The small waves on the shore lap up against your feet, but do not cause any movement. If you go to Hawaii however, and jump into the big surf – one of those 6 meter waves have enough energy to break every bone in your body. In the case of sound waves the energy is passed on as increases in air pressure.
Amplitude, also known as magnitude, is found on the vertical ‘y’ axis on the sine graph in Figure 2.2 above. The units on the sine graph have a maxima and minima of 1 and -1 respectively, but in noise measurements, these will change to either pressure (Pa) or decibels (dB). You will discover this in future chapters.
In the world of sound and noise, you would know amplitude as ‘volume’, such as that found on a stereo hi-fi, but really, volume is a knob or button that controls the amplitude of the sound pressure.
Wavelength, period, frequency & velocity
The wave created by the sound (independent of amplitude) will travel over a distance. The unit of distance used in sound measures is the meter (m). The distance travelled will take a certain amount of time, which is measured in seconds (s). So we have time and distance intertwined in a unique relationship, which can be expressed using the following equation;
ν=fλ
Where;
V = velocity (m/s)
F = frequency (c/s)
L = wavelength (m)
Albeit, it is sometimes necessary to look a bit further into this simple equation to see all of its magic. Examine the worked example below;
Example 2.1
Assuming a constant velocity of ~340 m / s (which it is not, but for our simple needs we shall think it is), then we can rearrange the equation to solve for both f and as follows;
f=ν/λ
So, assuming v = 340 m / s, and = 0.2 m, then the frequency is;
f = 340 / 0.2
= 1700 c / s
And the wavelength can be calculated using;
λ=ν/f
So, assuming v = 340 m / s, and f = 1000 c / s, then the wavelength is;
λ = 340 / 1000
= 0.34 m
Obviously all of these values change slightly if we report the speed of sound accurately.
Sometimes this concept is best seen pictorially, as seen in Figure 2.3 below where other concepts are explained such as the period etc.
Figure 2.3 – Sine wave showing 10 cycles in 0.001 seconds at a velocity of 340 m/s. The interactive version of this graph can be found in the Noise-theory-manual spreadsheet.
In this image, the y axis (amplitude) is set to 85 decibels, the x axis (time) covers 0.001 seconds. In this timeframe the wave travels 10 cycles (count them). A cycle is from one point in the wave to the next equivalent point. The time this takes is called the period, which is measured as the number of seconds per cycle (s/c). The period of the waveform above can be calculated in one of two ways;
P=t/c or P=1/f
We can use the first formula to work out the period from the graph above;
P = time (s) / number of cycles
= 0.001 / 10
= 0.0001 s/c
The frequency is described as the reciprocal of the period, that is the number of cycles per second, which is actually far more informative than the period is, so it is the frequency that is usually calculated from such things and is expressed in the unit of Hertz (Hz) The frequency can therefore be calculated as;
f=1/P
From the information above, this is calculated as;
f = 1 / P
= 1 / 0.0001
= 10000 c/s (Hz)
The wavelength is the length of one period of the waveform, which is from one point in the wave to the next equivalent point, and as mentioned is measured in meters (m). Now that we know the frequency, we can calculate the wavelength assuming a velocity of 340 m/s;
λ = v / f
= 340 / 10000
= 0.034 m
The sine wave
Now that you know the basics of waves, we can move on to slightly more complex issues. A sine wave, in its most simple form can be constructed from the following formula;
u=A∙sin((2πft)-θ)
Where;
u = position of a point in the wave
A = Amplitude, i.e. 'height' of the wave from the center
sin = Excel's SIN (sinusoidal) function
π = Excel's PI function
f = Frequency, as Hz or c/s or s-1
t = Time, seconds
Θ = Phase, or 'offset', sort of irrelevant to us.
Relax, you don’t need to know how to use this formula, you just need to be aware that a whole heap of information can be derived from it.
From this, we can calculate several other important variables such as the period, time, wavelength, angular frequency, wavenumber and the list could go on. The important variables are found below;
ω = 2πf Calculates the angular frequency (r/s)
T = 2πω Calculates the period (seconds per wave s/ λ)
λ = ν/f Calculates the wavelength in meters (m)
k = 2π/ λ Calculates the angular wavenumber (r/ λ)
Interactive spreadsheet
Now would be a good time to work with the sine wave simulator in the interactive spreadsheet called Noise-theory-manual on the Physics 3 tab. This will allow you to visualise the sine wave and its properties in action.
The sine wave and its phase shifted cousin the cosine, are very important in science, and go a long way to explaining the behaviour of sound and noise. In the world of sound, the sine wave in Figure 2.3 above would represent a phenomena known as a pure tone, which is a ‘perfect sound’, and although rarely (if ever) found in nature, the pure tone can be generated on a device called an oscilloscope.
This goes a long way to understanding noise because sine waves (and cosine waves) can be added together. Consider Figure 2.4 below. The top figure is a sine wave of frequency 30 Hz and the middle figure is a cosine wave of frequency 3. When added together they make a new sound with multiple frequencies as seen in the bottom figure.
Figure 2.4 – Adding sine and cosine waves to get a ‘noisier’ signal. Imagine noise as many hundreds of these signals added together. From Noise-theory-manual spreadsheet.
It turns out that complex waveforms of noise are nothing more than lots of sine and cosine waves ‘added together’ (sort of), and if they can be added together, then they can be ‘pulled apart’ (sort of – it’s a lot more complex than this but we can ignore).
Most sounds are made up of a combination of many frequencies. Even the notes of musical instruments are complex waveforms made up from many different frequencies. Most everyday noise consists of a wide mixture of frequencies. This is commonly referred to as broad band noise. When the noise has frequencies evenly distributed throughout the audible range it is known as white noise. This sound is somewhat like the sound of water near a waterfall.
How complex waveforms are pulled apart to reveal their composite frequencies is by way of a computer algorithm called a Fast Fourier Transform, the understanding of which is beyond the scope of this course, but needless to say it is the sole reason that we can analyse the frequencies of complex waveforms such as those found with noise.
You might be asking yourself...
“Didn’t we just calculate the frequency above using the formula f=1/P?”
Yes, but that only works for pure tone sine waves. For really complex waveform signals, we cannot separate the individual waves out, so we need to use the FFT! This is how noise meters work.