Digital sound files are not made up of sine waves - You may be thinking of FM or West Coast synthesis where sine waves are used to modulate other sine waves to generate more complex waveforms.
You will often see two different values associated with digital sound: the sample rate and the bit depth.
The bit depth determines the range of values available - on a CD this is 32,767 or 16 bit. At any given moment, a value somewhere between 0 and 32,767 is fed into the digital-to-analogue converter (DAC) to give a voltage that can be used to push a speaker cone in or out by a specific amount.
The sample rate determines how fast these values follow each other. Going back to CDs, a sample rate of 44.1kHz means that the values being fed to the DAC are being sent at a rate of 44,100 values per second.
Alternating between 0 and 32,767 at 44,100 times per second would result in a 44.1kHz square wave passing through the DAC.
Human hearing doesn't really work above around 18kHz-20kHz so we have twice the samples that we need - this helps to eliminate any issues with harmonics introduced by the digitisation process (similar to pixelation on a low res picture). You've probably heard this as a metallic or crunchy sound in low-quality digital audio.
The higher the sample rate and bit depth, the greater the fidelity of the recording/playback. There is a point, however, where the difference in quality becomes imperceptible to human hearing.
I forgot to add that the different file formats (FLAC, MP3, WAV) etc. use different algorithms to calculate which sets of values they can skip without losing quality.
Removing unused values means that the resulting files can be smaller but the DAC needs to know what criteria were used in deciding which samples to remove so that it can calculate and insert an appropriate replacement value during playback.