Changes in the sampling rate directly affect the file size of an audio file. The sampling rate, which is the number of samples of audio carried per second, determines how frequently the analogue sound wave is captured in the digital domain. A higher sampling rate results in more samples per second, thereby increasing the amount of digital information needed to represent the sound, and consequently, the file size.

For instance, doubling the sampling rate will approximately double the file size. This is because the audio file now contains twice the number of samples for the same duration of audio. The impact on file size is substantial when dealing with long recordings or large music libraries. For applications where file size and bandwidth are constraints, such as streaming or portable media, a lower sampling rate might be chosen to keep file sizes manageable. However, this comes at the cost of potentially reducing the quality of the audio, particularly the ability to accurately reproduce higher frequencies. Therefore, choosing the appropriate sampling rate is a balance between the desired audio quality and practical considerations like storage and bandwidth.

Choosing different bit depths for audio recording and playback has significant implications on the dynamic range and noise level of the audio. Bit depth, which refers to the number of bits used for each sample, directly impacts the sound's dynamic range - the difference between the quietest and loudest parts of the audio. A higher bit depth increases the dynamic range, allowing for a greater range of volume levels in the recording. For example, a 16-bit audio, common in CDs, provides a dynamic range of about 96 dB, while a 24-bit audio, used in professional settings, offers a dynamic range of around 144 dB.

The choice of bit depth also affects the noise floor of the recording. A higher bit depth results in a lower noise floor, meaning that the recording will have less inherent noise and a clearer sound. This is particularly important in professional music production, where capturing the subtle nuances of sound is critical. However, for everyday use and consumer-grade applications, 16-bit audio often suffices. Ultimately, the choice of bit depth should be guided by the requirements of the intended application, considering factors like the desired dynamic range, noise floor, and file size.

The Nyquist Theorem, a fundamental concept in digital signal processing, states that to accurately represent a continuous signal (like sound) in a digital format, it must be sampled at least at twice the rate of its highest frequency component. This theorem underpins the entire process of sound sampling and is crucial for avoiding aliasing, a form of distortion that occurs when higher frequency components of the sound are misinterpreted as lower frequencies due to insufficient sampling rate.

In the context of digital audio processing, adhering to the Nyquist Theorem ensures that all the audible frequencies (generally up to 20 kHz for human hearing) are accurately captured in the digital representation. For instance, CD audio, with its sampling rate of 44.1 kHz, more than satisfies the Nyquist criteria for human hearing. Sampling at a rate below the Nyquist limit would lead to a loss of information and a resultant decline in sound quality. Thus, understanding and applying the Nyquist Theorem is essential for anyone involved in digital audio processing, as it is key to preserving the integrity of the sound during the digitisation process.

Lossy and lossless compression are two methods used in reducing the file size of audio data, each impacting audio quality differently. Lossless compression, as the name suggests, compresses the audio data without any loss of quality. Techniques like FLAC (Free Lossless Audio Codec) and ALAC (Apple Lossless Audio Codec) are used, which allow the original data to be perfectly reconstructed from the compressed data. This method is preferred when audio quality is paramount, such as in professional music production. However, lossless compression has a limitation in the amount of reduction it can achieve, often resulting in larger files compared to lossy compression.

Lossy compression, on the other hand, significantly reduces file sizes by permanently removing certain parts of the audio data deemed less important or less perceptible to the human ear. Formats like MP3 and AAC are examples of lossy compression. This method can achieve much smaller file sizes, making it suitable for streaming and storing large music libraries. However, the downside is the irreversible loss of audio quality, which can be noticeable at higher compression rates. The choice between lossy and lossless compression depends on the balance one wishes to strike between file size and audio fidelity.

Choosing between different audio file formats like WAV, MP3, and AAC involves several considerations, primarily revolving around audio quality, file size, and compatibility.

• WAV: A standard format for uncompressed audio in Windows environments. It offers the highest quality since it is lossless and uncompressed, retaining all the audio data as recorded. However, this results in large file sizes, making it less practical for portable devices or streaming. WAV is often used in professional settings where audio quality is of utmost importance.
• MP3: A popular compressed and lossy format. It significantly reduces file size by removing parts of the audio not easily perceivable by human ears. This makes MP3 files ideal for consumer use, such as in portable media players and online streaming. However, the compression can affect audio quality, especially at lower bit rates.
• AAC: Stands for Advanced Audio Coding and is similar to MP3 but with better sound quality at similar bit rates. AAC is the default format for Apple devices and services. It offers a good balance between audio quality and file size and is well-suited for streaming and portable devices.

The choice of format depends on the intended use of the audio file. For archival and professional use where quality is paramount, uncompressed formats like WAV are preferred. For everyday listening, where storage and bandwidth are limited, compressed formats like MP3 and AAC are more suitable. Compatibility with playback devices and software is also a key consideration in selecting an audio file format.