Previously we took a look at sound pressure. Sound pressure is a field quantity,
changes based on the distance from the source, and can be easily measured using a microphone or
some other pressure sensitive transducer. In this video, we'll talk all about sound power
and on all 3 points, sound power is completely different. It is a power or energy quantity,
and not a field quantity. There is no concept of distance when talking about sound power,
it is independent of directionality and is independent of distance from the observer or
the source. It is a constant value no matter what the environmental conditions are. And sound power
is a theoretically calculated value, which can't easily be measured by a single device.
So based on these starting points, you might think that they are totally unrelated concepts.
But there is a cause and effect relationship between them.
We previously looked at a heater analogy, but this time, let's look at light. A light bulb is rated
to some electrical power. An led light rated to a power of 10Watts produces some amount of light. It
doesn't matter whether the 10w led light is in a small room, or in a large room or in a closed box.
The 10w rating will remain the same, wherever the bulb may be. The intensity of the light emitted
might be different at different distances from the source, but the source itself remains unchanged.
It continues to emit light at a constant rate. The 10W that represents the power rating on the bulb
is a calculated value and it’s easy to see the advantages of such a rating. With it, you could
make an apples to apples comparison. Given the design and manufacturing process is the same,
you can clearly compare 3 different led lights, rated at 1W, 10W and 100W. Based on this alone,
you can make decisions about where to use, what kind of space, requires what rating of light.
You don’t need to measure the intensity of light produced at different spatial locations,
you could just calculate that value just knowing the power rating and the space you are in.
So, as can imagine, the sound power or acoustic power is quite an important measure in the field
of acoustics. Since sound power is a constant non directional value, it’s possible to compare
the sound output of different devices, without any knowledge of the environment in which they
were tested or the distance at which measurements were taken. This makes sound power levels ideal
for product labeling, for comparing the sound emission of different power tools for example.
If an operator were to use a pneumatic drill for instance, if he knows the sound power generated
from this tool, he would know the appropriate level of ear protection to use and the maximum
time that he can spend on the equipment in one go to meet health and safety guidelines
and to prevent long term hearing damage. You could theoretically compute the Sound
pressure level at any distance from a source, just by knowing the sound power of the source.
So an acoustic consultant could then determine if the resulting noise emissions from a construction
side would adversely affect a nearby residence and will comply with the relevant regulations, or
if mitigation measures should be designed or different, quieter, machinery should be chosen.
All that is well and good. But for audio engineers and producers, sound power is not a particularly
useful metric to know. Power ratings are also applied to loud speakers and monitors,
but that’s electrical power, and not sound power, and we’ll get to that at some point
of time. But I choose to go further with this topic, because this is the first time
we’re dealing with representing and quantifying a power quantity. So far, we’ve only looked at
sound pressure, which is a field quantity. So let’s dig a little deeper. Acoustic sound power
is the total airborne acoustic energy emitted by a device over unit time. It’s measured in Watts.
Acoustic power levels of many devices are quite small. For example, a noisy coffee grinder may
emit only about 5 milliWatts of acoustic power. On the other hand, a rocket at take off could produce
100 million Watts of sound power. The range of values sounds power can take on is massive!
So naturally, we want to represent these values in the logarithmic scale,
or better yet, the decibel scale. A bel is said to be log of the ratio between
two power quantities. Perfectly suited for our needs. And a decibel is just one tenth of a bel.
And since the decibel is a relative scale of values, we need to pick the reference power level
against which all other power levels are measured. What do we pick for the reference value?
But before that, we want the power level in decibels to be comparable to pressure level
in decibel.Since they are dimensionless units, we want some means of comparing between the two,
we don't want to have these values completely different from each other.
To achieve this, we need to have similar conditions when choosing the reference value.
When choosing the reference value for sound pressure, we chose the minimum pressure value
that a good pair of ears could just about hear a 1khz sine tone in an anechoic chamber.
This value was established to be 20micro pascal. Now, the question is, what is the power required
to generate this pressure value from the same measuring distance. The complicated
answer to this question is 10 power -12 watts or 1 picowatt, which is a tiny infinitesimal value.
But that’s the value we need to plugin as the reference. So there you go.
The Formula for sound power level in decibels, or SWL. But wait, if you’ve
watched the previous video, we derived the sound pressure level or SPL, and it had this formula.
Why is one value multiplied by 10, and the other by 20? It’s a bit confusing
isn’t it? In Fact if you look at a lot of other decibel units, they’re all similar,
but they have the same quirk. What do you use? 10 or 20? How do you keep track of all of them?
The simple answer is you have to identify whether the unit you’re looking at is a
power quantity or a field quantity. Power quantities always have a multiplier of 10
and field quantities always have a multiplier of 20. That’s because, in the real world, the power
quantities are directly proportional to the square of the field quantities.
So, sound power is directly proportional to square of the pressure. And electrical
power is directly proportional to the square of the voltage or the square of the current.
And the log of a squared quantity, is just 2 times the log of the quantity. Makes sense?
So I previously mentioned that by knowing the sound power of a source,
you can theoretically calculate the sound pressure caused by it at any distance.
I say theoretically, because the formula assumes an ideal space,
where the source is suspended in mid air, with no primary or secondary reflections of any kind.
In the real world, these sort of spaces are hard to come by,
but engineers make clever modifications to the formula to fit the space being measured.
We’ll not get into that. But we know that sound power is directly proportional to
the square of the sound pressure. Let’s bring back a couple constant terms that were ignored.
Here r is the distance from the source, and 4pir2 is actually the area of a sphere,
we’ll see how this is important when we talk about Sound intensity. And Q is called the directivity
factor, and is just 1, when we consider a spherical free field for sound propagation.
And here’s the amended formula for sound pressure level in decibels. Just by looking at it,
it sort of makes sense. Sound pressure level is equal to sound power level, minus some amount. As
the distance from the source increases, the larger this term gets, and the smaller the sound pressure
level is. But when you move closer to the source, the pressure level increases, until you are right
up against the source, where the sound pressure level is the exact same as the sound power level.
This is a unique condition, the distance you’d need to be from the source to have the
sound power level equal to the sound pressure level is 0.282m for a directivity of 1.
Ok, so, I’m not entirely sure how useful this information is for a lot of people out there.
But it is interesting for sure, and a solid fundamentals backing goes a long way. So I’ll
talk about a few more of these theoretical topics before we get into the meat of bones
of audio level measurements in computers, which you’re probably more interested in.
Coming up next is sound intensity.