This has more to do with the device you’re using to put the sound in your ears. If you’re using bluetooth hearing protection that is at least a little quality, then the only thing that happens is the music gets drowned out a little bit.
There is to some extent play between the soundwaves of specific frequencies canceling out the same frequencies the headphones are supplying.
Regular earbuds or ones with noise canceling and all that jazz?
A riding lawnmower makes noise, and the noise it makes is more on the bass end than the treble end. As such, bass from your music get’s combined from bass from your lawn mower, and lawnmower is pretty loud so it can drown it out.
Also, if it’s just plastic earbuds and not in-ears (silicone tips), you don’t have much isolation, which is what you want for hearing protection (over-ear & closed-back headphones are going to be best; like the Sony or Bose headphones if you want wireless and active noise canceling).
There are three bones in each ear which transmit sound from the eardrum to the cochlea (the part that converts sound into nerve impulses that or brain can interpret). Muscles connect to two of those bones. They contract when we hear loud noises (or expect to hear loud noises, like chewing, sneezing, or yelling) to protect the cochlea. That makes the bones transmit mostly high frequencies. When exposed to a continuous loud rumble (like your lawnmower or on an airplane), everything else sounds tinny.
[Not ELI5 explanation](https://www.sciencedirect.com/topics/immunology-and-microbiology/tensor-tympani-muscle)
You really should wear hearing protection if you’re noticing this effect. The tiny muscles eventually get fatigued and you start damaging your hearing. If you still want to listen to music, try a Bluetooth hearing protector, or get decadent with the ones using active noise suppression.
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