Stars with hot Jupiters tend to be rotating faster than other stars of the same age and mass. This trend has been attributed to tidal interactions between the star and planet. A constraint on the dissipation parameter $Q_star$ follows from the assumption that tides have managed to spin up the star to the observed rate within the age of the system. This technique was applied previously to HATS-18 and WASP-19. Here we analyze the sample of all 188 known hot Jupiters with an orbital period $< 3.5$ days and a cool host star ($T_{eff} < 6100$ K). We find evidence that the tidal dissipation parameter ($Q_star$) increases sharply with forcing frequency, from $10^5$ at 0.5 day$^{-1}$ to $10^7$ at 2 day$^{-1}$. This helps to resolve a number of apparent discrepancies between studies of tidal dissipation in binary stars, hot Jupiters, and warm Jupiters. It may also allow for a hot Jupiter to damp the obliquity of its host star prior to being destroyed by tidal decay.
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