The gear mesh frequency is calculated by...

The gear mesh frequency is determined by multiplying the number of teeth on the gear by the rotational speed of that gear. This frequency represents the rate at which the teeth of the gear mesh together during operation, which is critical for analyzing vibrational signatures and diagnosing potential issues in machinery.

When gearing operates, the interaction of the gear teeth generates vibrations at specific frequencies directly related to the number of teeth and how fast they are spinning. This calculation helps professionals identify normal operating conditions and detect anomalies, such as misalignment or wear, by monitoring vibration frequencies.

In contrast, the other options do not correctly reflect the relationship between gear teeth and rotational speed. Adding the number of teeth on each gear does not yield a relevant frequency; rather, it provides a summation without any bearing on the movement or interaction between the gears. Dividing the number of teeth on the input gear by those on the output gear would give a gear ratio, which is not directly related to frequency calculations. Multiplying the number of teeth on each gear also fails to relate to the actual frequency heard in operational conditions, as it does not account for the rotational speed, which is a crucial element in the calculation.