[MUSIC]
[MUSIC]

Okay, in this tutorial, we're going to visit the notion of LEQs, Okay?
Okay, in this tutorial, we're going to visit the notion of LEQs, Okay?

Now that's the symbol for the LEQ.
Now that's the symbol for the LEQ.

The A here stands for A weighting, BQ stands for
The A here stands for A weighting, BQ stands for

equivalent continuous, and t time period of LEQ.
equivalent continuous, and t time period of LEQ.

We know that there's formula to predict this figure, okay?
We know that there's formula to predict this figure, okay?

It's 10 log 10 to power L1 over 10 times t1,
It's 10 log 10 to power L1 over 10 times t1,

plus 10 to the L2 over 10 times t2 etc.,
plus 10 to the L2 over 10 times t2 etc.,

divided by capital T.
divided by capital T.

I'm just gonna consider one term in this tutorial, okay?
I'm just gonna consider one term in this tutorial, okay?

So the L1 here is a sound pressure level, or
So the L1 here is a sound pressure level, or

sound intensity level that you've been exposed to for a certain time period t1.
sound intensity level that you've been exposed to for a certain time period t1.

So for example, it could be that you're exposed
So for example, it could be that you're exposed

to 90 decibels, for say 2 hours, okay?
to 90 decibels, for say 2 hours, okay?

Now in this particular tutorial,
Now in this particular tutorial,

what I'd like to do is to consider rearranging that formula for t1, okay?
what I'd like to do is to consider rearranging that formula for t1, okay?

Now this is actually something that we do quite often in this course.
Now this is actually something that we do quite often in this course.

And the reason why we do this is that when we look at noise at work regulations, we
And the reason why we do this is that when we look at noise at work regulations, we

often have to look at the maximum LEQ that you can be exposed to, which is 85 db.
often have to look at the maximum LEQ that you can be exposed to, which is 85 db.

We often look at situations in the working environment where
We often look at situations in the working environment where

somebody might be working at, say 95 or 96 decibels.
somebody might be working at, say 95 or 96 decibels.

And we want to know how long they can spend in that working environment
And we want to know how long they can spend in that working environment

before they reach the legal limit of 85.
before they reach the legal limit of 85.

So what we have to do then is to rearrange this particular formula here for
So what we have to do then is to rearrange this particular formula here for

t1, so this tutorial will do just that.
t1, so this tutorial will do just that.

So the first thing we need to do in all formulas whereby we need to
So the first thing we need to do in all formulas whereby we need to

get to a term in the log term, in this case it's t1.
get to a term in the log term, in this case it's t1.

We need to first of all isolate the log term.
We need to first of all isolate the log term.

So at the moment we've got a 10 in front of it.
So at the moment we've got a 10 in front of it.

So we have the LEQ here, we'll leave that as it is, we divide that by 10.
So we have the LEQ here, we'll leave that as it is, we divide that by 10.

So what we've done is simply moved the 10 across.
So what we've done is simply moved the 10 across.

We've kept everything there in the brackets,
We've kept everything there in the brackets,

we've not moved anything at all, just the 10.
we've not moved anything at all, just the 10.

The other thing we need to do now is to get rid of this log term.
The other thing we need to do now is to get rid of this log term.

If you remember the rules of logs,
If you remember the rules of logs,

one of the things that we use is something called antilogs.
one of the things that we use is something called antilogs.

Antilog is simply a way of getting rid of the log term, okay?
Antilog is simply a way of getting rid of the log term, okay?

If we get rid of this log term here,
If we get rid of this log term here,

we need to do the equivalent action to this side here.
we need to do the equivalent action to this side here.

So in this particular case here, when we antilog this side
So in this particular case here, when we antilog this side

it simply becomes ten to the power of the LEQT divided by ten.
it simply becomes ten to the power of the LEQT divided by ten.

So that's going to be 10 to the power of all that, equals,
So that's going to be 10 to the power of all that, equals,

when you antilog a log term, the log just simply disappears.
when you antilog a log term, the log just simply disappears.

So all we end up with is this term here.
So all we end up with is this term here.

So nothing has changed apart from the fact that we've eradicated the log.
So nothing has changed apart from the fact that we've eradicated the log.

Now we look at something we can rearrange with a bit more simplicity.
Now we look at something we can rearrange with a bit more simplicity.

We're after t1, so what we can do here,
We're after t1, so what we can do here,

I'm going to go to the end of this screen here.
I'm going to go to the end of this screen here.

T1 is there so I'll just put a line here to separate these,
T1 is there so I'll just put a line here to separate these,

we've still got this 10 to the LEQ, Over 10, there.
we've still got this 10 to the LEQ, Over 10, there.

Take the big T across, which is gone to there.
Take the big T across, which is gone to there.

We take this term here down to the bottom.
We take this term here down to the bottom.

So all we've done is switch these terms around.
So all we've done is switch these terms around.

So this formula is particularly useful when we want to find the time period that
So this formula is particularly useful when we want to find the time period that

you can be exposed to at a certain level, before you reach the legal limit.
you can be exposed to at a certain level, before you reach the legal limit.

So the legal limit would be say, 85 here, and that would be for 8 hours, okay?
So the legal limit would be say, 85 here, and that would be for 8 hours, okay?

So the big T here would be 8 hours, this would be 85.
So the big T here would be 8 hours, this would be 85.

And this would be the desired level, or the level that you're working at, okay?.
And this would be the desired level, or the level that you're working at, okay?.

So that could be anything above the 85 value.
So that could be anything above the 85 value.

Okay, and that completes that short tutorial.
Okay, and that completes that short tutorial.