Practice Page

The Wave Equation

$$ v = \lambda f $$

• Note that wavelength is represented by the Greek letter lambda or \( \lambda \).

Fill out the tables below to practice using the formula above.

1. Catherine shakes a slinky with a frequency of 4 Hz. The waves have a speed of 5 m/s. What is the wavelength?
   
2. 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?
   
3. Henry creates waves with a wavelength of .55 m, and a speed of 3 m/s. What is the frequency of these waves?
   
4. 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: $$ d = vt \; \; \; \; \; \; \; \; \; \; v = \lambda f $$

1. Howard creates waves with a frequency of 4 Hz and a wavelength of 0.33 m.
   1. How fast do the waves move?
   2. How far do the waves move in 5 seconds?
2. Timothy creates waves with a frequency of 6 Hz and a wavelength of 0.8 m.
   1. How fast do the waves move?
   2. How far do the waves move in 12 seconds?
3. Bobby creates a wave with a wavelength of 2 meters. It moves a distance of 100 meters in a time of 5 seconds.
   1. What is the speed of the waves?
   2. What is the frequency of the waves?
4. Susan creates a wave with a frequency of 55 Hz. It moves a distance of 200 meters in a time of 0.6 seconds.
   1. What is the speed of the waves?
   2. 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: $$ \text{frequency} = \frac{\text{number of waves}}{\text{time}} $$

1. If there are 6 waves in 3 seconds, what is the frequency of the waves?
2. If there are 15 waves in 5 seconds, what is the frequency of the waves?
3. If there are 12 waves in 5.42 seconds, what is the frequency of the waves?
4. There are 3 waves in 7.25 seconds, and the wavelength of the waves is 0.89 meters.
   1. What is the frequency of the waves?
   2. What is the speed of the waves?
5. There are 5 waves in 8.25 seconds, and the speed of the waves is 2.2 m/s.
   1. What is the frequency of the waves?
   2. What is the wavelength of the waves?

Answers: