RIAA is actual an abbreviation of Record Industry Association of America, an organisation, as the name indicates, has its roots back in the childhood of the gramophone industry.
The necessary RIAA playback equaliser characteristic curve has three frequency references: 50, 500 and 2120 Hz. These frequencies correspond to the time constants 3180, 318 and 75 µs respectively, see the figure below. More about RIAA can be found here.

It is an endless list for realizing the RIAA playback
characteristic and the necessary amplification. In
the following you will find a calculator for determining the component
values of the RIAA network for passive equalization. In
the figure
below, the equalization network consist of the components R0, C0, R1
and C1 between the two amplifier stages.
In reality the output impedance of the
first amplifier
section is not
zero, and the input impedance of the second amplifier section is not
infinite. Assuming we are using just resistive values of
the
output impedance, RS in the figure below, and the input impedance RL,
it is quite easy to modify the value of R0. However, we must assume we
know the values of RS and RL.

Here, the easiest way to find the RIAA
network
component values, is
by choosing C1:
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Knut Harald Nygaard