Question

you notice that a wave completes 1.2 cycles in 2.5 seconds. what is the period of the wave?

Explanation:

Identify given values

We are given the following values from the problem statement:

• Number of cycles completed, \(N = 1.2\text{ cycles}\)
• Total time elapsed, \(t = 2.5\text{ seconds}\)

Define the target unknown

We need to find the period of the wave, denoted by \(T\). The period is the time required to complete one full cycle.

State the formula for wave period

The period \(T\) is defined as the total time divided by the number of completed cycles:

$$T = \frac{t}{N}$$

Calculate the period

Substitute the given values into the formula:

$$T = \frac{2.5\text{ s}}{1.2}$$

$$T \approx 2.0833\text{ s}$$

Round to appropriate significant figures

Since the given values \(1.2\) and \(2.5\) both have two significant figures, we round our final answer to two significant figures:

$$T \approx 2.1\text{ s}$$

Answer:

\(2.1\text{ s}\)