What is the wavelength (in m) of the waves you create in a swimming pool if you splash your hand at a rate of 3.00 Hz and the waves propagate at 0.650 m/s?

To find the wavelength (\(\lambda\)) of the waves in the swimming pool, we can use the relationship between wave speed (\(v\)), frequency (\(f\)), and wavelength:

\[
v = f \cdot \lambda
\]

Rearranging to solve for \(\lambda\):

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

### Given values:
- Frequency (\(f\)) = 3.00 Hz
- Wave speed (\(v\)) = 0.650 m/s

### Calculation:
\[
\lambda = \frac{0.650 \, \text{m/s}}{3.00 \, \text{Hz}}
\]
\[
\lambda = 0.2167 \, \text{m}
\]

### Answer:
The wavelength of the waves is approximately **0.217 meters**.

Would you like more details on the calculation or have any other questions?

Here are five related questions you might find interesting:
1. What happens to the wavelength if the frequency is increased to 5.00 Hz?
2. How does the speed of waves in water compare to sound waves in air?
3. What would the wavelength be if the speed were doubled?
4. How does wave frequency affect the amplitude of the waves?
5. Can you calculate the wavelength if the wave speed was 1.00 m/s?

**Tip:** Remember, wavelength decreases when frequency increases if the wave speed remains constant!

Learn how to calculate the wavelength of waves in a swimming pool when you splash your hand at 3.00 Hz and the waves propagate at 0.650 m/s. This problem applies the wave equation, suitable for students in Grades 9-11.

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