Hertz (Hz)

Also called Hz, Cycles per second

The hertz is the SI unit of frequency, equal to one cycle per second, which makes it an inverse second. A frequency of 50 Hz means fifty complete repetitions every second.

Count the complete repetitions in one second and the answer is in hertz. Dimensionally there is nothing left on top:

1 Hz=1 s−11\ \text{Hz} = 1\ \text{s}^{-1}

A cycle is not a unit, so it does not survive. All four AP tables of information print T=1/fT = 1/f, which is the same statement rearranged: at 5050 Hz one cycle lasts 1/50=0.0201/50 = 0.020 s.

The trap is radians per second. Angular frequency ω\omega is also an inverse second dimensionally, is also a rate of oscillation, and is not measured in hertz. The two differ by one full turn:

ω=2πf\omega = 2\pi f

So a 2.02.0 Hz oscillator has ω=4π≈12.6\omega = 4\pi \approx 12.6 rad/s. Substitute 12.612.6 where 2.02.0 belonged and the answer is out by a factor of 2π2\pi, with no unit mismatch to warn you, because the radian is dimensionless. Anything sitting inside a sine or cosine as ωt\omega t wants rad/s. Anything a question calls hertz, cycles per second or revolutions per second is ff.

Range. The prefixes matter here, because the same unit covers audible sound at tens or thousands of hertz and green light at 550550 nm, which the sheet's λ=c/f\lambda = c/f puts at f=(3.00×108)/(550×10−9)=5.5×1014f = (3.00 \times 10^8)/(550 \times 10^{-9}) = 5.5 \times 10^{14} Hz.

Hertz is one of seven unit symbols printed on all four AP tables of information, along with joule, kilogram, meter, newton, second and watt.

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