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?

3 answers

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.

no

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!