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# Units of Frequencies and Wavelengths

by Ron Kurtus (revised 2 March 2015)

The characteristics of a waveform are that it has an amplitude, wavelength, frequency and velocity. The amplitude is the height of a wave or its intensity. The wavelength is the distance between amplitude maximums. The frequency is how often the maximums or crests move past a given point. And finally, the velocity—or how fast the wave is moving—is the product of the frequency times the wavelength (v = fλ).

The units of frequency are in hertz (Hz) or its multiples. The units of wavelength are in meters, its multiples or fractions of a meter. As the frequency increases, the wavelength decreases, provided the velocity is kept constant. For example, waves at extremely high frequencies have very short wavelengths.

Exponential powers of 10 are used when frequencies or wavelengths become very large. Very short wavelengths are designated as a negative exponentials.

Questions you may have include:

• What is the exponential notation with 10?
• What are the frequency terms?
• What are the wavelength terms?

This lesson will answer those questions. Useful tool: Units Conversion

## Powers of 10

A convenient way to express large and small numbers is to use exponents or powers of 10, which are multiples of 10.

### Large numbers

You can designate a large number such as 1,000,000 as an exponent or power of 10 by counting the number of zeros and writing the number as 106 or 1*106.

If the number was 300,000,000, you would write it as 3*108.

If the number was 2,524,200, you would round it off and use the scientific notation of a number less than 10, with two decimal places, such as the approximate value of 2.52*106..

Other equivalent notations for a number such as 3*108 are 3*10^8 and 3E8.

### Small numbers

Following the same method for a small number 1/100,000 = 1/105, since 100,000 has 5 zeros. That can be written as 10−5. Note that the decimal version of 1/100,000 is 0.00001, which only has 4 zeros after the decimal point. It is something to be aware of. Some other examples are:

3/10,000,000 = 0.0000003 = 3*10−7

0.00252 = 2.52*10−4

0.000000004026 rounds off to 4.03*10−9

## Frequencies

Frequencies are measured in hertz (Hz), which means cycles or wave crests per second. You can write the frequency with the symbol versions, as a large number or as an exponent.

Symbol Number Exponent
1 Hz (hertz) 1 Hz 1 Hz
1 kHz (kilohertz) 1000 Hz 1*103 Hz
1 MHz (megahertz) 1,000,000 Hz 1*106 Hz
1 GHz (gigahertz) 1,000,000,000 Hz 1*109 Hz

The frequency of some waveforms such as a tsunami water wave, can cycle very slowly. In such a case, the frequency may be designated in cycles per minute or hour. 1/3600 Hz is 1 cycle per hour.

## Wavelengths

Wavelengths are usually expressed in the metric or SI system, since having multiples of 10 are more convenient. Wavelengths can range from many kilometers long to extremely short lengths or fractions of a meter.

Name Meters Exponent
1 km (kilometer) 1000 m (meters) 1*103 m
1 m 1 m 1 m
1 cm (centimeter) 0.01 m 1*10−2 m
1 mm (millimeter) 0.001 m 1*10−3 m
1 μm (micrometer or micron) 0.000001 m 1*10−6 m
1 nm (nanometer) 0.000000001 m 1*10−9 m
1 Å (Angstrom) 0.1 nm 1*10−10 m

## Summary

The relationship between frequency and wavelength is that—for a given speed—as the frequency increases, the wavelength decreases. At extremely high frequencies, you can have very short wavelengths.

As frequency numbers get very large, they are designated by phrases such as "mega" and "giga" or by powers of 10. A very short wavelength is designated as a negative exponential.

## Resources and references

Ron Kurtus' Credentials

### Websites

Wave Motion Resources

### Books

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