Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 4.0 s. when one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves determine the speed of the wave.

Options

A. `2.5 m//s`
B. `5 m//s`
C. `40 m//s`
D. `4 m//s`

Explanation

To determine the speed of the wave created by the two canoes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Period of the Wave:**
The problem states that each canoe bobs up and down with a period (T) of 4.0 seconds.

\[ T = 4.0 \, \text{s} \]

2. **Calculate the Frequency of the Wave:**
The frequency (f) is the reciprocal of the period. We can calculate it using the formula:

\[ f = \frac{1}{T} = \frac{1}{4.0 \, \text{s}} = 0.25 \, \text{Hz} \]

3. **Determine the Distance Between the Canoes:**
The problem states that the two canoes are 10 m apart. When one canoe is at its highest point, the other is at its lowest point. This means they are separated by half of the wavelength (λ/2).

\[ \text{Distance} = \frac{\lambda}{2} = 10 \, \text{m} \]

4. **Calculate the Wavelength:**
From the distance, we can find the wavelength (λ) by rearranging the equation:

\[ \lambda = 2 \times \text{Distance} = 2 \times 10 \, \text{m} = 20 \, \text{m} \]

5. **Calculate the Speed of the Wave:**
The speed (v) of the wave can be calculated using the formula:

\[ v = f \times \lambda \]

Substituting the values we found:

\[ v = 0.25 \, \text{Hz} \times 20 \, \text{m} = 5 \, \text{m/s} \]

### Final Answer:
The speed of the wave created by the canoes is **5 m/s**.

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