Wave Relationships worksheet - Free Printable

Problem Description:

The task is to count the number of wavelengths shown in each wave function depicted in the images. A wavelength is defined as the distance between two identical points on a wave (e.g., crest to crest or trough to trough).

Solution Approach:

1. Understand the Definition of Wavelength:
- A wavelength is the distance between two consecutive identical points on a wave, such as from one crest to the next crest or from one trough to the next trough.

2. Analyze Each Wave:
- Carefully observe each wave and count the number of complete wavelengths visible in the image.
- A complete wavelength is identified by tracing from one point (e.g., a crest) to the next identical point (the next crest).

3. Count the Wavelengths:
- For each wave, identify the starting point and trace along the wave to count how many times you encounter an identical point before reaching the end of the wave.

Step-by-Step Analysis of Each Wave:

#### Wave #1 (Red Wave):
- The wave starts at a crest and ends at a crest.
- Count the number of crests: There are 3 complete crests.
- Therefore, there are 3 wavelengths.

#### Wave #2 (Purple Wave):
- The wave starts at a crest and ends at a crest.
- Count the number of crests: There are 10 complete crests.
- Therefore, there are 10 wavelengths.

#### Wave #3 (Blue Wave):
- The wave starts at a crest and ends at a crest.
- Count the number of crests: There are 6 complete crests.
- Therefore, there are 6 wavelengths.

#### Wave #4 (Green Wave):
- The wave starts at a crest and ends at a crest.
- Count the number of crests: There are 8 complete crests.
- Therefore, there are 8 wavelengths.

#### Wave #5 (Orange Wave):
- The wave starts at a crest and ends at a crest.
- Count the number of crests: There are 4 complete crests.
- Therefore, there are 4 wavelengths.

Final Answer:

\[
\boxed{3, 10, 6, 8, 4}
\]

Explanation:

Each wave was analyzed by identifying the starting point (a crest) and counting the number of times the wave returned to an identical point (another crest) before reaching the end of the wave. This method ensures accurate counting of the wavelengths.