I wanted to double check to see if I am reading this correctly. The way the pot is connected:

the output of the first op-amp connects to the inverting input of the second op amp through 10k resistance. Call this R1.

The pot varies the resistance seen from the inverting input of the second op amp to the 8 ohm speaker. Call this Rvariable.

If these connections are correct, how does Rvariable vary from the 10k. Is it from 10k down to ~ 0 ohms?

Thanks!

 

If the volume control pot on the left schematic is adjusted so that the wiper is all the way towards the right opamp, then the inverting (-) input is connected to the output of the opamp, which turns the opamp into a voltage follower. The output of the opamp will then track the noninverting (+) input; since that input is connected to ground, the output will follow ground, and no signal will be output to the speaker.

If the pot is adjusted all the way the other way, the inverting input will be connected directly to the output of the left-hand opamp, and so the feedback from the output of the amp will be ineffective. This will make the amplifier operate open-loop, so it will have maximum gain. The output will be overdriven, and the signal will be clipped badly.

There should be some fixed resistance between the output of the 1st opamp and the 10k pot to prevent the amp from operating without feedback.

Your LTSpice schematic on the right is different from the schematic with the pot; as you appear to be keeping R2 at 10k, and changing RVariable. You should keep the total value of both resistors close to 10k. If you set one resistor to 1k, the other should be set to 9k, etc. You can't specify a value of 0 for a resistance, but you can assign it a low value, like 1m

Look here in our E-book:
http://www.allaboutcircuits.com/vol_3/chpt_8/4.html
Read about negative feedback on the above page, and divided feedback on the next page. The divided feedback page explains how to calculate the gain of the amplifier by resistance values.

 

I see. I hope I am understanding this correctly. I re-drew the images for the 2 states you described.

So, the pot is altering the resistances from the output of op amp #1 to the inverting input of op amp #2 and from the inverting input of op amp #2 to the output. If we move the pot all in the way in one direction, we see the full 10k resistance on one side, and basically a short on the other side. And vice versa.

If the pot is operating somewhere in between, then the 10k resistance gets split into the two paths. Like the LTSpice schematic I posted, only the total resistance is 10k, divided to the two paths.

Please correct me if I am mistaken. I feel pretty dumb right about now just asking something so simple

 

Yes, you have it.