https://file.aiquickdraw.com/mathbot/file/17298088966749irbty18.jpg

The diagram in the image represents the displacement of a wave as a function of time. To calculate the frequency of the wave, we can use the formula:

\[
f = \frac{1}{T}
\]

Where:
- \( f \) is the frequency in Hertz (Hz).
- \( T \) is the period, which is the time taken for one complete wave cycle.

### Step-by-Step Solution:
1. From the graph, one complete cycle (from one peak to the next peak) occurs between \( t = 0 \) seconds and \( t = 2 \) seconds.
   
   Therefore, the period \( T \) is:
   \[
   T = 2 \, \text{seconds}
   \]

2. Using the formula for frequency:
   \[
   f = \frac{1}{T} = \frac{1}{2} = 0.5 \, \text{Hz}
   \]

### Answer:
The correct frequency of the wave is **0.5 Hz**, which corresponds to option **C**.

Would you like further details or have any questions?

### Related questions:
1. What is the relationship between wave period and wavelength?
2. How does wave amplitude affect the energy of the wave?
3. What are the factors that influence the speed of a wave?
4. How does frequency relate to the pitch of a sound wave?
5. Can frequency be used to determine the color of light?

**Tip:** Frequency and period are inversely related. The shorter the period, the higher the frequency, and vice versa.

What is the frequency of the wave shown in the displacement-time graph?

Learn how to calculate the frequency of a wave based on a displacement-time graph. This example uses the formula f = 1 / T, where the period T is determined from the graph. Suitable for students in Grades 9-12.

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