And to be equal,

something has to come over here,

has to be the divider of one over Time.

Because this is a DDT and that is energy,

therefore that has to be one over time constant which we do not know yet.

Okay that is nice.

And this has to be because the energy is coming out,

this has to be,

this has to be cannot be positive.

Energy has to be decay.

I mean, energy cannot increase so it has to be minus.

Now, this is a very simple differential equation and we do know the solution and

E reverberant is equal

to initial energy which I denote to be zero,

and exponential decay minus T over time.

Oh that's very pretty obvious.

That means when I hit sound over there,

then the energy is exponentially decay like you

may hear the sound is decaying very rapidly with the some time constant.

So. this is very simple straightforward result.

The physical meaning is that,

the sound in the room can characterize this train time constant tau.

In other words, tau determines room acoustics,

or tau determines the quality overall, in other words.

So, what is tau? So, if you look at

this equation when tau is large than energy,

and tau is large then

the energy is rapidly decaying or slowly decaying when tau is large.

Say tau is 100 then the energy is slowly decaying.

When tau is small,

the energy will decay very rapidly.

And then, Sabine did the experiment again and he found that interestingly,

that tau is proportional to the size of room and open area window, As.