Considering a sample of 20 eclipsing binary systems with delta Scuti type primaries, we discovered that there is a possible relation among the pulsation periods of the primaries and the orbital periods of the systems. According to this empirical relation, the longer the orbital period of a binary, the longer the pulsation period of its pulsating primary. Among the sample, the masses of the secondaries and the separations between the components are known for eight systems for which a log P-puls versus log F (the gravitational pull exerted per gram of the matter on the surface of the primaries by the secondaries) diagram also verifies such an interrelation between the periods. So, as the gravitational force applied by the secondary component onto the pulsating primary increases, its pulsation period decreases. The detailed physics underlying this empirical relation between the periods needs further confirmation, especially theoretically. However, one must also consider the fact that the present sample does not contain a sufficiently large sample of longer period (P > 5 d) binaries.