Gravitational waves near the source are incredibly tiny in amplitude. The amplitude of a gravitational wave is a measure of the strain or distortion it induces in spacetime. The strain is defined as the fractional change in length along one direction caused by the wave.
The gravitational waves that have been detected thus far, such as those observed by the LIGO and Virgo detectors, have amplitudes on the order of 10^(-21) or smaller. This means that as the gravitational wave passes through a detector or observer, it causes a strain of about one part in 10^21 in the length of the space being measured.
To put this into perspective, the strain induced by gravitational waves is incredibly small compared to the size of everyday objects. For example, a gravitational wave with an amplitude of 10^(-21) passing through a kilometer-long object would cause a length change of only about 10^(-18) meters, which is far smaller than the size of an atomic nucleus.
However, it's important to note that gravitational waves become larger as they propagate away from their source. As gravitational waves travel through spacetime, they can accumulate energy and grow in amplitude, but this growth is typically very gradual. Only when gravitational waves originate from extremely powerful cosmic events, such as the merger of two black holes or neutron stars, do they generate detectable signals by the time they reach Earth-based detectors.
In summary, gravitational waves near their source are incredibly small in amplitude, causing minuscule distortions in spacetime. It is only as they propagate and accumulate energy over large distances that their amplitudes become detectable.