How two tones relate to each other comes down to the ratio between how fast each one vibrates. The study of sound therefore starts with counting vibrations and comparing them as simple number ratios, before it turns to the objects that make the sound.
Sound is best understood as three separate stages. First a body vibrates, then that vibration travels through air or another gas, and finally an ear turns it into a sensation. The hearing of animals as well as humans belongs inside the subject, not outside it.
Strings, plates, bells and air columns each have their own characteristic patterns of vibration, and those patterns depend on the object's shape and material. They can be studied by experiment, for example by drawing a violin bow across a glass plate and watching how it vibrates.