Signal to noise in the search for gravitational waves

Schnabel responds: Bruce Schulte’s letter argues that reducing instrumental noise by a factor of 1.5 does not increase the volume of space from which an event can be detected by a factor of 1.5³ ≈ 3. The information given by Johanna Miller, however, is correct.

For gravitational-wave observatories, both signal and noise sources are usually quantified in terms of signal and noise amplitudes, not in terms of powers as is common for receivers of electromagnetic waves. Thus the signal strength is proportional to the strain of spacetime caused by a gravitational-wave event and is inversely proportional to the observer’s distance from the source. The square root, which Schulte’s letter mentions, is thus already included in figure 2 of the Physics Today story . Note that the y-axis is labeled GEO600 NOISE (relative strain) per square root Hz. Miller’s text also provides the value for the achieved noise reduction in power. It was 3.4 dB, which corresponds to a factor of 2.2, whose square root is 1.5.