Explanation of Units of Frequencies and Wavelengths - Succeed in Physical Science. Also refer to hertz, megahertz, gigahertz, exponent, waveform, micrometer, micron, nanometer, Angstrom, physics, Ron Kurtus, School for Champions. Copyright © Restrictions
Units of Frequencies and Wavelengths
by Ron Kurtus (17 March 2008)
The units of frequency of a waveform are in hertz (Hz) or its multiples. The units of wavelength are in meters, its multiples or fractions of a meter. Since the velocity of a waveform equals its frequency times its wavelength (v = fλ), as the frequency increases, the wavelength decreases, keeping the velocity constant. At extremely high frequencies, you can have very long wavelengths and vice versa. 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 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. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Powers of 10
A convenient way to express large and small numbers are 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 to 2,500,000 and give its approximate value as 2.5*106. Although 25*105 is the same number, the convention is to keep the first number under 10.
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
0.0025 = 25 * 10−3 = 2.5*10−4
0.000000004025 rounds off to 0.000000004 = 4*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 long wavelengths and vice versa. 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 an exponential.
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Mini-quiz to check your understanding
1. Why would a number be expressed as 5*107?
2. What does the word "mega" mean in megahertz?
3. Which is larger: a cm or mm?
If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.
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Units of Frequencies and Wavelengths