V440 Per: the longest-period overtone Cepheid

V440 Per is a Population I Cepheid with a period of 7.57 d and low-amplitude, almost sinusoidal light and radial velocity curves. With no reliable data on the first harmonic, its pulsation mode identification remained controversial. We obtained a radial velocity curve of V440 Per with our new high-precision and high-throughput Poznan Spectroscopic Telescope. Our data reach an accuracy of 130 m s(-1) per individual measurement and yield a secure detection of the first harmonic with an amplitude of A(2) = 140 +/- 15 m s(-1). The velocity Fourier phase (21) of V440 Per is inconsistent at the 7.25 Sigma level with those of fundamental-mode Cepheids, implying that the star must be an overtone Cepheid, as originally proposed by Kienzle et al. Thus, V440 Per becomes the longest-period Cepheid with securely established overtone pulsations. We show that a convective non-linear pulsation hydrocode can reproduce the Fourier parameters of V440 Per very well. The requirement to match the observed properties of V440 Per constrains the free parameters of the dynamical convection model used in the pulsation calculations, in particular the radiative loss parameter.