Half power will result in -3dB sound level, that is acceptable.
But the writer of the article assumes that the speaker sensitivity is 90 dB @ 1W/1m, and no where describes the speaker as "the circular one, 8 ohms input resistance, found commonly in cheap electronics".
Can we still use the 90 dB value for our calculations ?
I think you will have to put the items together (tone source, amplifier and speaker) and get empirical.
I think with an efficient speaker, you'll get quite a bit of sound. On the other hand, amplifiers with more power are available, in small modular form, and are relatively inepensive.
I think the speaker itself will be the key component.
What is the desired goal for purpose for the sound?
I used a LM386 module . Powered it with a bench top power supply (5V) but whatever pot setting on the module I choose, there isn't any current draw greater than 20 mA. The 8 ohm, 0.5W speaker just isn't loud enough. It should draw 250 mA to consume 0.5W and the power supply is capable of providing 30W.
I am using Android based Sound meter app to check sound levels. If I hold my phone very close to the speaker the reading is around 60 dB. I also have a louder speaker in a product, whose sound levels I want to match and it gives a reading of around 80 dB.
What could be the reason, the speaker in my setup isn't consuming 250 mA and isn't loud enough ?
Beyond the LM380 and LM384 chips, which I have used and of course the LM386 since forever, I'd just be googling. Which I leave in your good hands.
^^ Looks like I fell asleep before hitting reply…
Now the LM386 can drive 4 ohms, so maybe try one (or two 8 ohm speakers in parallel), and it can take 12 volts (variants can take more) power supply, so perhaps providing that voltage to,power the amplifier will get you closer.