The Wave Equation
$$
v = \lambda f
$$
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Note that wavelength is represented by the Greek letter
lambda or \( \lambda \).
Fill out the tables below to practice using the formula above.
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Catherine shakes a slinky with a frequency of 4 Hz. The waves have a speed of 5 m/s. What is the wavelength?
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Bobby is very fast and shakes a rope 18 times a second. The wavelength of each wave is .4 m. What is the speed of waves in the rope?
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Henry creates waves with a wavelength of .55 m, and a speed of 3 m/s. What is the frequency of these waves?
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I have a wave with a frequency of 15 Hz, and a speed of 4 m/s. What is the wavelength?
Two-Step Problems:
Use two formulas together to solve the following problems:
$$
d = vt \; \; \; \; \; \; \; \; \; \; v = \lambda f
$$
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Howard creates waves with a frequency of 4 Hz and a wavelength of 0.33 m.
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How fast do the waves move?
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How far do the waves move in 5 seconds?
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Timothy creates waves with a frequency of 6 Hz and a wavelength of 0.8 m.
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How fast do the waves move?
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How far do the waves move in 12 seconds?
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Bobby creates a wave with a wavelength of 2 meters.
It moves a distance of 100 meters in a time of 5 seconds.
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What is the speed of the waves?
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What is the frequency of the waves?
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Susan creates a wave with a frequency of 55 Hz.
It moves a distance of 200 meters in a time of 0.6 seconds.
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What is the speed of the waves?
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What is the wavelength of the waves?
Using other formulas for frequency
The frequency of a wave is defined as the number of waves per second.
You can use this definition to write a new formula for frequency of wave:
$$
\text{frequency} = \frac{\text{number of waves}}{\text{time}}
$$
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If there are 6 waves in 3 seconds, what is the frequency of the waves?
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If there are 15 waves in 5 seconds, what is the frequency of the waves?
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If there are 12 waves in 5.42 seconds, what is the frequency of the waves?
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There are 3 waves in 7.25 seconds, and the wavelength of the waves is 0.89 meters.
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What is the frequency of the waves?
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What is the speed of the waves?
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There are 5 waves in 8.25 seconds, and the speed of the waves is 2.2 m/s.
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What is the frequency of the waves?
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What is the wavelength of the waves?
Answers: