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Searches for gravitational waves with km-scale laser interferometers ofteninvolve the long-wavelength approximation to describe the detector response.The prevailing assumption is that the corrections to the detector response dueto its finite size are small and the errors due to the long-wavelengthapproximation are negligible. Recently, however, Baskaran and Grishchuk (2004Class. Quantum Grav. 21 4041) found that in a simple Michelson interferometersuch errors can be as large as 10 percent. For more accurate analysis, theseauthors proposed to use a linear-frequency correction to the long wavelengthapproximation. In this paper we revisit these calculations. We show that thelinear-frequency correction is inadequate for certain locations in the sky andtherefore accurate analysis requires taking into account the exact formula,commonly derived from the photon round-trip propagation time. Also, we extendthe calculations to include the effect of Fabry-Perot resonators in theinterferometer arms. Here we show that a simple approximation which combinesthe long-wavelength Michelson response with the single-pole approximation tothe Fabry-Perot transfer function produces rather accurate results. Inparticular, the difference between the exact and the approximate formulae is atmost 2-3 percent for those locations in the sky where the detector response isgreater than half of its maximum value. We analyse the impact of such errors ondetection sensitivity and parameter estimation in searches for periodicgravitational waves emitted by a known pulsar, and in searches for an isotropicstochastic gravitational-wave background. At frequencies up to 1 kHz, theeffect of such errors is at most 1-2 percent. For higher frequencies, or ifmore accuracy is required, one should use the exact formula for the response.

High-frequency corrections to the detector response and their effect on searches for gravitational waves