A woman is standing in the ocean, and she notices that after a wave crest passes, five more crests pass in a time of 50.0 s. The distance between two successive crests is 32 m. Determine, if possible, the wave's period and wavelength.

Options

A. 0.0200s, 64m
B. 0.100s, 16m
C. 10.1s, 32m
D. 50.0s, 8.0m

Answer

To solve the problem step by step, we will determine the wave's period and wavelength based on the information provided.

### Step 1: Understand the given information
- The woman observes that after one wave crest passes, five more crests pass in a time of 50.0 seconds.
- The distance between two successive crests (wavelength) is given as 32 meters.

### Step 2: Determine the time period of the wave
The time taken for five crests to pass is 50 seconds. Since the time period (T) is the time taken for one complete wave cycle (one crest to the next crest), we can express the time for five crests as:
\[ \text{Time for 5 crests} = 5T = 50 \text{ seconds} \]

To find the time period \( T \):
\[ T = \frac{50 \text{ seconds}}{5} = 10 \text{ seconds} \]

### Step 3: Identify the wavelength
The distance between two successive crests is defined as the wavelength (\( \lambda \)). According to the problem, this distance is given as:
\[ \lambda = 32 \text{ meters} \]

### Conclusion
- The wave's period \( T \) is **10 seconds**.
- The wavelength \( \lambda \) is **32 meters**.

### Summary of the Solution
1. The time taken for five crests to pass is used to find the time period of one wave.
2. The distance between successive crests is directly given as the wavelength.