Ok, the "heartbeat" sound (as it's often referred to) you are hearing is part of the entrainment beats. Generally these are just a low background sound and you don't consciously hear them, unless you have the volume turned up, in which case they become more obvious. It's not necessary to have the volume turned up, as the ears and brain are perfectly capable of hearing and discerning the beats from the foreground sound of the track. Some entrianment beats are inaudible though others are audible. If I've got this the right way around, the isochronic and monaural beats can be heard, and this is why they can be listened to without headphones but still have effect, though they may be 'incorporated' into the sounds of the track so that they are not that obvious; conversely, the binaural beats require headphones because the frequencies/sound waves need to reach the ears at the right time where they are combined by the brain and the resultant binaural frequency is created by the brain itself (it's created by the left and right frequencies being slightly out of step, causing a type of resonance).
Of course the technicalities can vary depending on how they've been created in the tracks and whether they are being done as sounds alongside the "sounds of nature" or incorporated into the actual "sounds of nature" itself.
Now, the two different headphones...
What is recommened is that you use headphones that do not alter the sound in any way from how it was originally recorded. Some headphones have built in equalizers or bass cancelling, or noise cancelling etc. to try and improve the quality of what you're listening to... which is fine for music or movies etc. but when dealing with tracks where the frequencies themselves are an integral part of the purpose of what you're listening to, you don't want any 'technology' to go and change things.
It could be that one of your headphones is altering things and the other isn't, but you'd have to look at the specification of the headphones. I would guess that the studio quality headphones are designed for clean feedback of exactly what was recorded, whereas the others are trying to alter things a little and hence negating out the entrainment frequencies somewhat.
If you're not sure, post what make and model headphones you're using and people here can go take a look at the specs for them and see if we can advise.
Hugs
Giles
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