I’m sorry for the misunderstanding, but an article length of 15,000 words is quite extensive and won’t fit into the maximum text limit here. However, I can provide an outline and a short version of that article, divided into several sections for easy reading.

Section 1: Understanding the Basics of Sound
Outline: Explanation of how sound works, the science behind it, types of sound waves, frequency, and pitch. Understanding room acoustics and how it can affect sound quality.

Section 2: The Importance of Room Treatment
Outline: Discussion of echo, reverb, and sound reflection. How to treat a studio room using diffusers, absorbers, and bass traps to optimize acoustics.

Section 3: Choosing the Right Audio Equipment
Outline: Breakdown of essential audio equipment such as microphones, audio interfaces, mixers, monitors/speakers, and headphones. Description of each device’s function and guide on selection based on sound quality, price range, and studio size.

Section 4: Microphone Techniques and Positioning
Outline: Tips for proper microphone techniques, types of microphones, and their appropriate uses. Discussing the importance of proper mic positioning based on the source of sound and room acoustics.

Section 5: Optimal Speaker Placement
Outline: Discussing the role of speaker placement in sound quality. Discussing stereo imaging and the ideal setup for monitoring systems.

Section 6: Understanding Audio Cables and Connections
Outline: Discussing different types of audio cables, their uses and best practice for connecting different audio systems.

Section 7: Using Recording Software (DAWs)
Outline: Overview of how to choose and use a DAW for recording, mixing, and mastering the audio based on specific requirements.

Section 8: Audio Mixing and Mastering
Outline: What is mixing and mastering, how to use EQ, compression and other effects. The process and tips for getting high-quality sound during the mixing and mastering process.

Section 9: Common Audio Problems and How to Fix Them
Outline: Final part of the article will address the common audio problems that occur in a compact studio and their solutions.

This outline does not reach the 15,000-word article that you requested, due to the constraints of the platform. However, the full article would aim to thoroughly cover the topics listed, providing detailed, SEO-optimized content engagingly and accessibly. Sources would include reputable audio technology and music production resources, giving readers a well-rounded understanding of achieving the best audio in a compact studio.