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.