As example: https://archive.org/details/Apollo10/10-030702_4-OF-6.wav Buzzing, sometimes pulsating and rather loud background sound, very annoying. Reminds me of old time dial-up modem or something like that. What is this? How I can filter it out, if possible?..
The performance of Apollo voice communications is discussed in Apollo Experience Reports D-6739 Voice Communications Techniques and Performance and D-6852 Communications System Flight Evaluation and Verification.
Both documents discuss interference in the voice signals, yet neither attempts to identify the source of the interference. Perhaps this is because it is futile to identify the exact source. Some of the potential sources:
Earth-based sources near the receiving antenna dishes. Two major stations were outside Madrid and Canberra, both capital cities of major nations. To reduce this effect, the dishes were placed in areas surrounded by mountains.
Spacecraft-based sources of noise. However, these would likely have been found during testing and on previous missions.
Interference from active noise reduction. The headsets including a second microphone to pick up ambient noise, which was then subtracted from the signal of the microphone near the astronaut's mouth. However, D-6739 reports that this tended to suppress the pilot's voice, not add other sounds.
Thermal noise from the vibrations of atoms is a well-known radio phenomenon. It was reduced by cooling the receiving antenna, but cannot be completely avoided. Further discussion follows.
Noise in radio equipment is expected, and the equipment is designed to process the signal in the presence of noise. We often talk about the "signal-to-noise ratio." You want to maximize the signal, which will depend on the power available to the transmitter. For the uplink to the spacecraft, the transmitter is on Earth and is there is more than enough power available for the signal. But the downlink from the spacecraft is limited to the spacecraft's power. This is why spacecraft downlinks are more susceptible to noise than uplinks. You also want to minimize the noise, which is addressed in the bullet points above.
D-6739 states that the Apollo voice downlink was designed for a signal-to-noise ratio of 14 decibels for primary communication links and 4 decibels for the backup links. These are equivalent to signal-to-noise voltage ratios of 5.0 (primary link) and 1.6 (backup link), respectively. So it's not surprising that the noise is audible.
Both papers also discuss problems with the squelch circuitry when on VOX mode. This was particularly a problem on Apollo 12 and 14. However, this would cause the astronauts' voices to cut out, not add additional noise.
Finally, the voice channel was also used for ranging tones. According to the Apollo Program Summary Report:
Because the VHF ranging requirement was added to the system late in the development program, certain limitations were imposed on the system to keep design modifications to a minimum. One limitation, a time-sharing of voice and ranging tones, resulted in a certain amount of voice distortion during ranging operation. Also, it was necessary to preclude all conversation during ranging acquisition. Preflight briefings and laboratory demonstrations for each crew helped to prevent flight problems because of these limitations.
D-6739 states that the ranging tone was a psuedorandom code at 30 kHz. That should be inaudible to humans. However, if digital sampling is not properly done, an effect called "aliasing" can occur which brings signals down in frequency. That might be the tone that you hear in the .WAV file.