Question

A buoy bobs up and down in the ocean. The waves have a wavelength of 2.5 m, and they
pass the buoy at a speed of 4.0 m/s. What is the frequency of the waves? How much time
does it take for one wave to pass under the buoy?

Answer 1

no

Answer 2

To find the frequency of the waves, we can use the wave speed equation, which relates the speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) of the wave:

\[
v = f \cdot \lambda
\]

Where:
- \(v\) is the speed of the wave (4.0 m/s)
- \(f\) is the frequency (which we are trying to find)
- \(\lambda\) is the wavelength (2.5 m)

Rearranging the equation to solve for frequency:

\[
f = \frac{v}{\lambda}
\]

Now, substituting in the values:

\[
f = \frac{4.0 \, \text{m/s}}{2.5 \, \text{m}} = 1.6 \, \text{Hz}
\]

So, the frequency of the waves is **1.6 Hz**.

Next, to find the time it takes for one wave to pass under the buoy, we can use the relationship between frequency and the period (\(T\)) of the wave:

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

Substituting the frequency we just calculated:

\[
T = \frac{1}{1.6 \, \text{Hz}} \approx 0.625 \, \text{s}
\]

Thus, it takes approximately **0.625 seconds** for one wave to pass under the buoy.

Answer 3

I apologize if my response was not clear or if I misunderstood your query. Let’s go through the calculations again step by step.

### Given data:
- Wavelength (\(\lambda\)) = 2.5 m
- Wave speed (\(v\)) = 4.0 m/s

### Step 1: Calculate the Frequency

The formula to calculate the frequency (\(f\)) of a wave is:

\[
f = \frac{v}{\lambda}
\]

Substituting the given values:

\[
f = \frac{4.0 \, \text{m/s}}{2.5 \, \text{m}} = 1.6 \, \text{Hz}
\]

### Step 2: Calculate the Time Period

The time period (\(T\)) is the reciprocal of the frequency:

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

Substituting the frequency calculated:

\[
T = \frac{1}{1.6 \, \text{Hz}} \approx 0.625 \, \text{s}
\]

### Summary of Results:
- **Frequency of the waves**: 1.6 Hz
- **Time taken for one wave to pass**: approximately 0.625 seconds

If there are any additional points or a specific aspect you would like me to clarify or correct, please let me know!