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So, I have a treadmill placed on a floor mat. The floor vibrates due to the force of running and my sofa vibrates due to this.
Not just treadmill, if I do cardio exercises on a rubber mat, the floor vibrates. Is there a technical way to figure out if the people downstairs can really hear it or not without asking them?
The most simple answer is: If you can hear it, they can hear it as well.
If you can't hear it, there's no way to know besides asking them.
In a physical sense, sound is a vibration of air. It spreads in all directions from its point of origin. It can cause objects to vibrate as well (that's how microphones work) and can be spread further by objects that transmit the vibration.
If you stomp your foot on your floor, the origin of sound is the floor where your foot lands. From there, the sound waves spread up to your ear, but also down to your downstairs neighbor and sideways through the floor (which makes your couch vibrate). The path to your neighbor is probably somewhat blocked by their ceiling, but in general that doesn't dampen sound much.
If the vibration of your couch is audible to you, you can be sure it's also audible to your neighbor. If the rubber mat causes inaudible vibrations, then their ceiling lamp might still swing like a pendulum or the vibrations might make some glassware clank. The safest way to know for sure is to ask.
Another method that involves a lot of guesswork is comparison. What kinds of sounds can you hear from your neighbor? Can you hear them talk, walk around or call someone on the phone? Then they can probably hear sounds from your appartment that are equally as loud.
The risks with this method are:
If your neighbor complains about the noise or vibrations, it might help putting the treadmill in another spot, preferably in a corner or at least very close to a wall. The structure of a house is stronger where walls and floors meet, which can at least avoid interferences.
If you know the people, visit them one day and have someone else use the treadmill while you are in their house. You should be able to find out if you can hear it as long as the part of their house that is beneath your treadmill is accessible to you. If you are unsure, move your treadmill to an area of your house where you know you will be able to hear it in their house.
