Simple Microphone....

You are making no sense.. Wave amplitude = voltage? Piezo sensor = piezo transducer/speaker/beeper disc?
Transistor as an unbiased emitter follower with no emitter resistor and with collector voltage reduced by potential divider resistors used as a volume control?
I believe a proper emitter follower would be a relatively proper "amplifier" to use for a piezo disc mike. Google for diagrams.

 

It's starting to clear now..
A sine wave has an amplitude (peak) of 1.414 times its rms value, that goes without saying.
An increase in (either) value will of course be perceived as an increase in loudness. The smallest difference you can make out is around 3dB (= twice the voltage).
A piezo transducer has a very high voltage output but also a very high impedance. It is after all a capacitor. To use its signal one has to amplify the current, not the voltage.
A fet is better at doing this than a bipolar transistor, but depending on what you have available & what you need to achieve, a bipolar is not a bad choice either.
An emitter follower circuit (wether made with a bipolar or a fet) has 0dB voltage gain (in=out) but a very high input impedance and a very low output impedance.
A bipolar emitter follower circuit (with a transistor gain of 300) can achieve almost the same performance as the fet circuit Steve suggested.

 

Yes. Resistor values will depend on the transistor gain. If you use 1Mohm for Rb and 10kohm for Re, that will require a transistor with a gain of 100, which is very common.
You'll want Vb & Ve to be around half of Vcc for maximum signal swing. So with the voltages being equal across each resistor you only need to select Rb 100 times Re.
(That is if the transistor has a gain of 100). You want to select the resistors as large as possible, and 10k is the most Re should be in order to easily drive the PC's ~50k.
Input (the mike) is Vin. Rs is just a representation of the mike's internal impedance, and can be disregarded. The capacitor is not needed here since the mike is a cap.
So you just connect the piezo disk straight to the base of the transistor. Your sound card is represented by Rl, and it's best to use that capacitor even if the PC has one.
C=1/(2*pi*f*Z) C= 1/(2*3.14*20*50k)=0.16uF. Use any value you have available close to that, it will only affect the low frequency. Speech only goes down to 150Hz btw.

 

Intuition, if you will, is based on knowledge one has picked up underway. In this case it's just basic electronics tuition that you'll find if you look around. There are tutorials right on this site, and this specific circuit is also called a common-collector amplifier btw. Common amplifier input impedances can be found by looking up some spec's.
Yes, those resistor values will be right for the transistor gain mentioned. Measure the actual voltages, and if they're not balanced then adjust resistor values accordingly.

Any Vcc voltage will do, and running it straight from 5V (or even 3V) should work fine. The Vcc value in itself is not what will reach (and potentially damage) the sound card.
Also, amplifiers (sound cards) have a maximum input value where they will clip, and another much higher value where they'll get damaged. I haven't checked actual values.
The piezo disks have such a high output that you might want to use the line input instead of the mike input btw.
Be aware that the disks are capable of very high voltage outputs, like if you tap or drop them they can generate 10's of Volts which could damage a sound card.

As for the map; hardly. Using that kind of projection won't get you anywhere using a straight line (as that will usually be "the long way home").

 

We do need some Zimbabweans, though.

 

The disc has all open edges where the sound pressure waves will pass around. Did you try to mount it by its edges in a hole (in a solid box or a baffle)?
The disc is quite stiff so it needs something to "kick" against in order to bend and do its work.
If it's still too weak for your application you can of course just try to plug it into the mic input of the sound card.
The airline headphones are of the dynamic type (meaning it's a moving coil in a magnetic field, having a low impedance (32 ohms) and hence a low signal level).
It can be plugged straight into the mic input but would probably need a common-emitter (or even better a common-base) amplifier to get a good signal level.