Frequency: How Many Waves Pass Each Second

A count, not a measurement

Wavelength and amplitude are distances you could measure with a ruler. Frequency is not: it is a count of how many complete waves go past in a second. That difference explains its unit, the hertz, which is simply one per second and is named after Heinrich Hertz, who first produced and detected radio waves.

Large frequencies get prefixes rather than long strings of zeros. A kilohertz is a thousand hertz and a megahertz is a million, so an FM station at 98.5 MHz is sending 98,500,000 waves past your aerial every second. Any calculation needs these converted back to plain hertz first.

Frequency and period are the same fact twice

The period is the number of seconds per wave and the frequency is the number of waves per second, so each is one divided by the other: f = 1 ÷ T and T = 1 ÷ f. On an oscilloscope you measure the width of one complete wave to get the period and invert it to get the frequency, because the screen shows time along the bottom.

A period of 0.02 seconds gives 50 hertz, which happens to be the frequency of the mains electricity supply in Pakistan and the United Kingdom alike. North America runs at 60 hertz instead, which is why some travel appliances carry both numbers on their label.

Frequencies worth carrying in your head

Frequency is what your ear reads as pitch and what your eye reads as colour, so a few reference values make the abstract number concrete. The most useful is the audible range: a healthy young human ear responds from about 20 Hz to about 20,000 Hz, or 20 kHz. The upper limit drops with age, which is why a teenager can sometimes hear a whine from a television that an adult in the same room cannot.

For light the same quantity decides colour rather than pitch, and the numbers are far larger: red light arrives at roughly four hundred million million waves per second and violet at nearly twice that. The idea has not changed, only the scale, which is why light frequencies are almost always quoted as wavelengths instead.

• 20 Hz – 20 kHz — the range a young human ear can hear
• Above 20 kHz — ultrasound, used for prenatal scanning, cleaning and depth sounding
• Below 20 Hz — infrasound, felt more than heard
• About 262 Hz — middle C on a piano; the A above it, 440 Hz, is the standard tuning note
• 50 Hz — the mains supply frequency in Pakistan and the UK
• 88–108 MHz — the FM radio band