Principles of Sound
The purpose of this thread is to discuss some basic fundamental principles of sound such as:
-How sound is a fluctuation of higher and lower pressure as it propagates through a medium
-Why a sound's intensity decreases with distance
-How sound intensity is represented on a logarithmic scale
-How your ear perceives a sound's frequency
What is Sound?
Sound is basically air moving as a systematic increase and decrease of air pressure (sound can also move through solids, water, etc but air is what we normally deal with). In our musical world, we can think of an object moving which causes the air to move around it. Think of an object (a string for example) moving back and forth, when the object moves forward it compresses the air in front of it and then when it moves back it rarefies the air in front of it. This creates a series of higher and lower pressures, which can be represented as a sine wave.
For the sake of saving time, here is a link with pictures and a better explanation of the basics of sound.
So the simplest sound can be represented as a sine wave that has amplitude and a wavelength. Amplitude represents how loud the sound is, (aka: it's intensity): the larger the amplitude of the wave, the louder the sound. Wavelength corresponds to the frequency of the sound (the pitch of the note): the shorter the wavelength the higher the note sounds.
1) Peak Amplitude
2) Peak to Peak Amplitude
3) RMS Amplitude (Not discussed)
This is a graph of two waveforms of the same frequency. The red wave would be considered louder than the black wave due to the red wave's larger amplitude.
This is a graph of two waveforms of the same amplitude. The red wave would be perceived as a higher note than the black wave due to the red wave's shorter wavelength.
Unfortunately real world noises, including most instruments we play, don't produce 'simple sounds'. Sounds we encounter in the real world are not made of one single frequency, instead they are made by multiple frequencies interacting with one another.
When we talk about more complicated sounds, with multiple frequencies interacting, then we refer to the lowest frequency in the sound as the 'fundamental' while the higher frequencies are called 'overtones'. The second highest frequency is called the 'First Overtone'; the third highest frequency is called the 'Second Overtone', etc.
It should be noted that there can be more than 3 overtones, and that different instruments produce overtones of different frequency and intensity. This complex frequency content is associated with the timbre/tone of the instrument* (which make a a guitar sound like a guitar and a cello sound like a cello, etc).
This is a graph of three separate waves of the same amplitude. These waves can also be considered individual overtones with the black wave representing the Fundamental, the red wave representing the First Overtone and the green wave representing the Second Overtone.
So the source of an instrument's voice is based on fairly simple mathematical principles, but when you add these simple waves together you get waves that look nothing like the original simple sine waves. Summing these simple waves together generates quite complex sounds.
This is a graph of the same three waves, but instead of being graphed separately they are summed together to produce a more complex waveform.
* - http://en.wikipedia.org/wiki/Timbre
The Near Field
Let's explore what a near field is because it is an important concept in sound theories. The near field represents an ideal listening environment, absent of any surfaces or imperfections that may reflect or interfere with our listening experience. When we invoke the near field in a thought process experiment we will consider no reflections or wave interference at all. You can think of a near field as floating in the air along with the source so that all we hear is sound from the source signal exactly as it is produced.
It is important to realize a near field is impossible to achieve. In real life you will have to deal with the environment and its impact on sound. However, the near field is a useful concept to help us simplify a thought experiment so that we pay attention to the concept we are trying to understand without compounding complications.
In a near field environment, sound intensity decreases directly to the square of the distance and this is called the inverse square law*. You can visualize this by thinking of a pebble being thrown into a pond and the waves moving away from the spot where the pebble was tossed in. The further the waves move away from source where the pebble was thrown in (the source), the smaller the waves get. The reason for this is because the pebble contacting the water creates a disturbance with a particular energy and the intensity of the energy is distributed across the wave(s) moving away from the disturbance. The waves move away from the source forming an ever-widening circle around it, and the intensity of the initial splash is distributed around this ever-widening circle.
* - It should be noted that this visual aid shows the sound intensity being distributed over the surface of a sphere, which is a more correct description
Continuing with the idea of thinking about sound intensity being related to the height of a water wave, it is important to note that humans have an incredibly large 'dynamic range' in our hearing perception. This means that humans can hear sounds that have quite a small wave height and we can hear sounds that have a very large wave height. To give you an example using our water wave analogy, suppose a sound made a 1 inch high wave that was just barely perceptible to our ear. If the 1 inch tall wave is the smallest sound we can hear than the human ear is also capable of hearing a sound 100,000 times greater or roughly 1.57 miles high. Now you would not be able to hear this very loud sound and the very soft sound at the same time though. Louder sounds have the ability to mask smaller sounds, but the amount of masking is dependent upon a number of factors (how simple the sounds are, the frequency range the sounds are active in, etc).
Now that we know that humans have a large dynamic range in our loudness perception, we can see that it can easily become unwieldy dealing with numbers that represent a linear representation of sound intensity. In order to make the numbers more manageable most people use a decibel scale when referring to sound intensity. A decibel scale is simply a logarithmic representation of a ratio between the intensity of two different sounds. Here is a few values showing the difference in power between two sound sources in the decibel scale compared the linear scale
dB to linear power ratio
0 dB = 1
3 dB = 1.995
10 dB = 10
20 dB = 100
50 dB = 100,000
100 dB = 10,000,000,000
As you can see from the above figures, you can represent a ratio in power between 1 and 10 billion by using just 0 through 100 decibels. This can make numbers much more manageable when performing math and comparing sound sources.
It should be noted that this section disregards certain complex relationships between power, voltage and intensity in the decibel rating system. These relationships will be expanded upon later in another post.
Humans also have quite a large range of wavelengths, or frequencies of sound, that we can perceive. Humans can hear sounds from 20 Hz to 20,000 Hz, but this range significantly shrinks with age (for example I can only hear ~60 Hz to ~15,000 Hz at my current age). Just as importantly, the human ear does not treat all frequencies equally. Some frequencies, such as ~1,000 Hz, sound louder to us than all the other frequencies because our ear is more sensitive in this range.
There are particular charts and references (like A-weight curves) that will show you how your ear perceives the loudness of frequencies in comparison to one another. Your ear also treats simple and complex sounds differently as well. Certain masking phenomenon will work quite differently depending on if you are hearing a simple waveform or a waveform with many overtones.
Sound Power vs Sound Pressure
This is a confusing topic surrounding sound that we will try to address and clear up. Sound power represents the amount of sound energy a source radiates directly. However, the sound power does not take into consideration environmental factors at all. Sound pressure on the other hand is how the radiated sound interacts with the environment and is indicative of what our ears actually hear.
To give a more tangible example, let us compare sound to heat. A heater has a certain rating for output (btu or watt) that represents the intensity of the energy output of the device. But if you are standing in a room with the heat source someone asks you 'How hot is it in here?' your answer will most likely not match the output of the heat device.
The reason for this difference in device output and perceived temperature has much to do with heat interaction with the environment.
- Heat will be the most intense nearest the heating device, as you approach the heating device you will feel more heat.
- Heat distributes itself throughout the room, when you first turn on a heating device in a cold room it will take some time for the whole room to warm up.
- The shape of the room will come into play as to where the hotter air will end up, for example: a room with tall ceilings will take longer to heat because heat rises.
- The size of the room has to be considered when figuring out how long the room will take to heat up and what temperature the room will reach.
- Air flow or lack thereof, etc.
These factors all determine the temperature of the room and explain how a room may feel cold even though you have a heater with immense output.
Similarly, sound power can be compared to the output of the heater and sound pressure is loosely analogous to room temperature. When we measure sound power output of a speaker it may not match entirely with the perceived volume in a room because:
- Loudness should be the most intense the closer you are to the speaker, as you approach the speaker you will hear a more intense sound level (given a near field environment).
- Sound will be absorbed and reflected when it comes into contact with a barrier. The degree of absorption and reflection has to do with the characteristics of the material the sound comes into contact with.
- Lower frequencies of sound need a larger barrier to reflect them due to their longer wavelength.
- When sound gets reflected inside a room, waveforms can sum or cancel to create areas of higher or lower intensity.
- Reflections can also cancel out sound of particular frequencies (comb filtering) or create areas of constant pressure (standing waves).
These factors (and others) determine the quality and loudness of how a sound source will be perceived in a room and they help explain how a speaker cabintet may sound louder/more bass heavy/better or worse in one room than another. Therefore, sound pressure levels are very sensitive to environmental factors.
For more information on sound pressure:
reserved for even more content
and one last reserved post
i submitted two links (this one and the troubleshooting thread by R45VT) on the forum under content creation. also had some ideas on the rules section so i posted some stuff there.
that should be enough content right now, we'll get these through and add some more after that.
All of those posts were inadvertantly deleted.
Please resubmit one at a time. I think you and I and maybe a few others can take on R45VTs and then send yours to Arby911 and ragingkitty.
I will circle back with them to seek approval and then post the Hot Links.
Excellent thread idea Gumbi.
Deserves to get stickied.
thx, really appreciate that.
it's part of a new system getting implemented. we are calling upon people to submit content to contribute to the knowledge base of the forum. we have some really knowledgeable members and we'd love any knowledge they can share.
I havent read through the entire thing yet.. But this deserves a sticky.
Great job putting this all together!
This is likely the most intelligible explanation of sound I've ever read. Bravo mate.
once again, i appreciate all the responses. it's nice to know this may turn out to be useful. let me take a quick opportunity to explain what this thread is:
this thread is a submission to the UG Resource Center (RC). we are hoping to centralize content like this for quick accessibility through the RC.
This is one of the first thread up for approval in the RC, i hope to post another thread that will tie into this thread, based on this background information the next thread will show you how to calculate sound intensity output of amplifier/speaker setups.
Maybe add a picture of an SPL Chart? One including the spl levels as well as how long it would take for hearing loss to occur at that sound level.
I have a good one on my phone from my audio class, I'll put it in thie post/a different one later.
FWIW, I thoroughly vetted Gumbi's sound articles some time ago and wholeheartedly approve.
i can include one of those in the intensity section. if you post a pic, i'll include it. i have been thinking about revising the 2nd post with some more pics to help with visualizations anyway.
Pretty cool thread. Don't forget to address the effects of absorption on sound dissipation over distance, as the traditional formula for sound dissipation does not take into account the effects of absorption, which has screwed with my bass frequencies on more than one gig.
that is why i discussed the near field. this talk tries to stay away from generic propagation through materials, absorbtion, reflection, interference (constructive and destructive), and general interaction with the environment. some of that is covered in thread.
i am going to try to get this one passed first.
but if you'd like to write a blurb on air absorbtion on frequency response i will include it (citing you as the source). air absorbtion is something i don't really know much about.
I play through an open-back cabinet. How does math?
Roger that. The problem with absorption is that it is never a constant, as it depends on the various materials with which the sound interacts...not least of all those moving, oddly-shaped bags of water we call the audience. I'll see if I can come up with something useful, rather than theoretical.
Keep this one going!
i was thinking about doing that particular graphic actually. you can think about the sound like that ripple of water (but i'd be a 3 dimensional ripple) and the energy of that disturbance is spread all over the sphere, as a result in a near field the OB and CB cab would have fairly similar 'loudness'. if you put them in a real room the story changes and the sound coming out the back of that OB cab will reflect off the back wall and add quite a bit of volume to your sound.
placing an OB cab in the right spot can be considerably louder than a CB cab.
there is also strange refraction principles with the temperature or density of material as well. like how you can hear farther over a lake on a hot day because of the heat and water vapor bending the sound.
i'd appreciate anything you can drum up.
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