The amplitude of gravitational waves is determined by the energy and mass distribution of the source that generates them, as well as the distance from the source to the observer.
Gravitational waves are ripples in the fabric of spacetime caused by the acceleration of massive objects. When massive objects undergo rapid changes in their acceleration, such as during the merger of two black holes or the explosion of a supernova, they emit gravitational waves. The energy and mass involved in these dynamic events contribute to the amplitude of the resulting gravitational waves.
The closer the observer is to the source of gravitational waves, the larger the amplitude will be. This is because gravitational waves decrease in amplitude as they propagate through space. As the waves travel farther from the source, their energy is spread out over a larger area, causing a decrease in the observed amplitude.
It's important to note that the amplitude of gravitational waves decreases rapidly with distance, making them incredibly difficult to detect. Even powerful sources, such as merging black holes, produce very faint signals by the time they reach Earth. This is why the detection of gravitational waves required the development of highly sensitive instruments like the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo detector.