# Notes / Frequency Units

The basic frequency unit is 1 Hertz (Hz). If the frequency of some event is n Hz, it means that the event occurs n times per second (see Time Units). Thus, $1~\textrm{Hz} = 1 / \textrm{second} = 1~\textrm{second}^{-1}$. Each frequency value corresponds to a time period. For example, 20 Hz corresponds to 50 ms because

$$20~\textrm{Hz}= \frac{20}{1~\textrm{s}}= \frac{20}{1000~\textrm{ms}}= \frac{1}{50~\textrm{ms}}.$$

Some additional useful frequency units (with corresponding time periods) are presented in the below table:

UnitSymbolValue in HzTime period
TerahertzTHz$10^{12}$1ps
GigahertzGHz$10^{9}$1ns
MegahertzMHz$10^{6}$1us
KilohertzkHz$10^{3}$1ms
HertzHz11s
MillihertzmHz$10^{-3}$$10^{3}s MicrohertzuHz (\muHz)10^{-6}$$10^{6}$s
NanohertznHz$10^{-9}$$10^{9}s The common symbol for frequency is f. If we want to calculate the frequency of an event, we should divide the number of events by a time interval that contains all these events. For example, if something happens 42 times per day, it means that the frequency of the event is:$$ f=\frac{42}{1d}=\frac{42}{86400s}\approx 0.000486s^{-1}=486\mu \textrm{Hz}$\$

The frequency term is widely used in many physics and engineering disciplines. Here are some famous examples:

• Humans can hear sounds with frequencies between 20 Hz and 20 kHz.
• Visible spectrum (a part of the electromagnetic spectrum that is visible to the human eye) is about 430..770 THz. The frequency range for the yellow color is about 508..526 THz.
• 440 Hz is the frequency of the musical note of A above middle C (A440, the pitch standard).
• Communication with submarines uses extremely low frequency: from 3 to 30 Hz.
• Shortwave radio uses frequencies in the range 1.6..30 MHz.
• Frequency of a typical microwave oven is about 2.45 GHz.
• The most popular WiFi frequencies are about 2.4 GHz (802.11b/g/n/ax) and 5 GHz (802.11a/h/j/n/ac/ax).

If we are talking about waves and we want to draw these waves on a plot, the frequency can be easily compared by a glance. Let us consider the following figure:

In this figure, we can observe three waves with different frequencies:

• (a) Let’s say that the first wave is a “reference” wave with a frequency 1x
• (b) The second wave frequency is twice (2x) that of the reference one
• (c) The third wave has frequency = 8x (eight times more than the reference one; four times more than the second frequency)