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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

*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.*

**units of wavelength**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 **10 ^{6}** or

**1*10**.

^{6}If the number was **300,000,000**, you would write it as **3*10 ^{8}**.

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*10 ^{6}**..

Other equivalent notations for a number such as **3*10 ^{8}** are

**3*10^8**and

**3E8**.

### Small numbers

Following the same method for a small number **1/100,000 = 1/10 ^{5}**, since

**100,000**has

**5**zeros. That can be written as

**10**. Note that the decimal version of

^{−5}**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}

0.000000004026rounds off to4.03*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*10^{3} Hz |

1 MHz (megahertz) | 1,000,000 Hz | 1*10^{6} Hz |

1 GHz (gigahertz) | 1,000,000,000 Hz | 1*10^{9} 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*10^{3} 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.

Always do your best

## Resources and references

### Websites

### Books

**Top-rated books on Wave Motion**

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## Units of Frequencies and Wavelengths