Wavelength and Frequency
Calculations
Ck12 Science
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Printed: August 7, 2014
AUTHOR
Ck12 Science
www.ck12.org
C HAPTER
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Chapter 1. Wavelength and Frequency Calculations
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Wavelength and Frequency
Calculations
Define wavelength.
Define frequency.
Describe the characteristics of a wave.
Perform calculations involving wavelength and frequency.
Do you enjoy going to the beach?
During the summer, almost everyone enjoys going to the beach. They can swim, have picnics, and work on their
tans. But if you get too much sun, you can burn. A particular set of solar wavelengths are especially harmful to
the skin. This portion of the soar spectrum is known as UV B, with wavelengths of 280-320 nm. Sunscreens are
effective in protecting the skin against both the immediate skin damage and the long-term possibility of skin cancer.
Waves
Waves are characterized by their repetitive motion. Imagine a toy boat riding the waves in a wave pool. As the
water wave passes under the boat, it moves up and down in a regular and repeated fashion. While the wave travels
horizontally, the boat only travels vertically up and down. The Figure 1.1 shows two examples of waves.
A wave cycle consists of one complete wave –starting at the zero point, going up to a wave crest, going back down
to a wave trough, and back to the zero point again. The wavelength of a wave is the distance between any two
corresponding points on adjacent waves. It is easiest to visualize the wavelength of a wave as the distance from one
wave crest to the next. In an equation, wavelength is represented by the Greek letter lambda (λ). Depending on the
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FIGURE 1.1
(A) A wave consists of alternation crests
and troughs. The wavelength (λ) is defined as the distance between any two
consecutive identical points on the waveform. The amplitude is the height of the
wave.
(B) A wave with a short wave-
length (top) has a high frequency because more waves pass a given point in
a certain amount of time. A wave with
a longer wavelength (bottom) has a lower
frequency.
type of wave, wavelength can be measured in meters, centimeters, or nanometers (1 m = 109 nm). The frequency,
represented by the Greek letter nu (ν), is the number of waves that pass a certain point in a specified amount of time.
Typically, frequency is measured in units of cycles per second or waves per second. One wave per second is also
called a Hertz (Hz) and in SI units is a reciprocal second (s−1 ).
Figure B above shows an important relationship between the wavelength and frequency of a wave. The top wave
clearly has a shorter wavelength than the second wave. However, if you picture yourself at a stationary point
watching these waves pass by, more waves of the first kind would pass by in a given amount of time. Thus the
frequency of the first waves is greater than that of the second waves. Wavelength and frequency are therefore
inversely related. As the wavelength of a wave increases, its frequency decreases. The equation that relates the two
is:
c = λν
The variable c is the speed of light. For the relationship to hold mathematically, if the speed of light is used in m/s,
the wavelength must be in meters and the frequency in Hertz.
Sample Problem: Wavelength and Frequency
The color orange within the visible light spectrum has a wavelength of about 620 nm. What is the frequency of
orange light?
Step 1: List the known quantities and plan the problem.
Known
• wavelength (λ) = 620 nm
• speed of light (c) = 3.00 × 108 m/s
• conversion factor 1 m = 109 nm
Unknown
• Frequency
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Chapter 1. Wavelength and Frequency Calculations
Convert the wavelength to m, then apply the equation c = λν and solve for frequency. Dividing both sides of the
equation by λ yields:
ν=
c
λ
Step 2: Calculate
1m
620 nm ×
= 6.20 × 10−7 m
109 nm
c
3.0 × 108 m/s
ν= =
= 4.8 × 1014 Hz
λ 6.20 × 10−7 m
Step 3: Think about your result.
The value for the frequency falls within the range for visible light.
Summary
• All waves can be defined in terms of their frequency and intensity.
• c = λν expresses the relationship between wavelength and frequency.
Practice
Question
Read the material on the link below and answer the questions as they come up:
http://www.absorblearning.com/physics/demo/units/DJFPh064.html
Review
Questions
1. Define wavelength.
2. Define frequency.
3. What is the relationship between wavelength and frequency?
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amplitude: The height of the wave, the distance between the crest and the trough
crest: The peak of the wave
frequency: Is the number of waves that pass a certain point in a specified amount of time.
trough: The low point of the wave cycle.
wavelength: The distance between two successive peaks.
References
1. Piervincenzo Madeo (Flickr:piervix). http://www.flickr.com/photos/piervix/5957410296/ .
2. CK-12 Foundation - Christopher Auyeung. .
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