frequency
Frequency measures how often something repeats: how many complete cycles happen each second. Picture a hummingbird's wings beating dozens of times a second, or counting how many swings a pendulum makes in a minute. Where the period asks how long one cycle takes, frequency asks how many cycles fit into a second.
Precisely, frequency f is the number of cycles divided by the time taken, so f = 1 / T where T is the period. Its unit is the hertz (Hz), meaning one cycle per second. Frequency connects to angular frequency omega by omega = 2 pi f, because there are 2 pi radians in one full cycle.
You meet frequency everywhere: the pitch of a musical note (a higher note has a higher frequency), the dial of a radio station, and the 50 Hz or 60 Hz of household mains electricity. One common trap: do not confuse ordinary frequency f, measured in cycles per second (Hz), with angular frequency omega, measured in radians per second. They differ by a factor of 2 pi.
Concert pitch 'A' vibrates at f = 440 Hz, meaning 440 cycles per second. Its period is T = 1 / 440 = about 0.00227 s, and its angular frequency is omega = 2 pi (440) = about 2765 rad/s.
Higher frequency means shorter period and, for sound, a higher pitch.
Frequency f (Hz, cycles per second) and angular frequency omega (rad/s) are different quantities related by omega = 2 pi f; keep the units straight.