Tesla_33 wrote:I want to adjust the amplifier via the gain (db) to adjust the volume of the speaker in SPL (dB).
How do I convert the gain of the amplifier in terms of voltage into the Speaker volume ( sound pressure level ) in (dB).
You don't, because the two are not directly related. Other factors are involved and you haven't said what they are! So it's not a stupid question, it's just an incomplete question.
The acoustic output from the speaker, in terms of a Sound Pressure Level (SPL), is dependent on how much electrical power is being fed into it, how sensitive and efficient it is in converting that electrical power into acoustic power, and how far away from the speaker that sound is being measured.
The norm is to measure SPL at 1 metre, so we'll assume that's also the case for you.
The speaker sensitivity or efficiency is normally specified in terms of the SPL generated at 1 metre for for 1 Watt of input power. So it might be 90dB/W/m, say. Without that figure to hand you can't calculate anything, so step one would be to go and find that sensitivity figure for the particular speaker you're using.
And while you're at it, it might be handy to know the nominal impedance of the speaker as well, so that you can calculate the input power provided by the amplifier.
By the way, power amplifiers usually have a fixed, rather than variable gain. The adjustment of output power is normally provided by a variable input attenuator.
So you'll also need to know the amplifier's input signal voltage as well as the 'amplifier gain' and input attenuator setting.
Obviously, the attenuator/amplifier combination could have an overall gain of 30dB, say, but it won't generate any output power to feed to the speakers unless there is an input signal present... and the bigger that input signal the more voltage -- and thus the more power -- the amplifier will deliver to the speaker (up to its clipping level!).
Calculating the square of the amplifier's output voltage, divided by the speaker's impedance, will give the power going into the speaker. Multiply that figure by the speaker's sensitivity and you'll have some idea of the acoustic output level in SPL.
Of course, there are also other factors that can affect the actual SPL in the room, such as the physical design of the speaker cabinet, the position of the speaker within the room, and the specific frequency or frequency range that you're interested in.
For those reasons, a more pragmatic solution might be simply to measure the system's SPL for given input signal levels and amplifier gains, actually in situ, rather than trying to calculate them! ...But it all depends on what you're trying to achieve.