Hi, you can use the free software PhotoRec, which supports signature-based scanning of your files. It supports file types such as .mp3, .wav, .aif, among others. You can find the full list of supported file types here. Another option with higher chances of success is Disk Drill—it supports both file system pointer scanning and signature-based scanning. Disk Drill offers a more user-friendly interface with the ability to preview (listen to) found files and select which files to recover. In contrast, PhotoRec recovers everything it finds within the selected file formats. In terms of pricing, PhotoRec is free and open-source, while Disk Drill allows you to recover up to 500MB for free on the Windows version, after which you’ll need to purchase the Pro version for $89, which is available for both Windows and macOS.
We have a dedicated article on recovering audio files from SD cards. Don’t worry about the fact that it’s focused on SD cards—there’s no difference in the methods and steps for recovery from a USB flash drive. You can check out the article here.