Small enough to fit in your shirt pocket, it can also be placed on a flat surface to monitor the sound levels around it.
An alkaline battery will easily power it 20 or more hours.
Step 1: The parts needed
The 'brains' of this project is a LM358 general-purpose op-amp which costs under 30-cents. The first half of the circuit is an amplifier which boosts the 500-micro-volts from an electret mic to about 1-volt. This level is generally called 'Line-level' and can be used to drive our LEDs, an audio amp, or even the input pins of an Arduino processor.
The second half of the op-amp is used as a voltage-to-current converter, which limits the brightness of the LEDs to 10mA or less.
The complete list of parts is below:
LEDs. Any combination can be used, as long as their total forward voltages is less then 8. For example, you can have up to 4 amber LEDs with 1.8v Vf.
Electret microphone - I got mine on eBay for under 25-cent
LM358 - Op-amp (8-pin DIP). Also available on eBay.
2N4401 - NPN general transistor (other audio NPN-types will probably work as well)
10k resistor x 5
2.2k resistor x 1
470k resistor x 1 (Can also be 330k as labeled in the circuit)
100-ohm resistor x 1
9-volt battery and connector
Perf-board and mounting parts.
Total cost: $3 or less.