What is the wavelength of a wave frequency 262 Hz in water if the wave velocity is `1480 ms^(-1)` in water?

Answer

To find the wavelength of a wave given its frequency and velocity, we can use the formula that relates these three quantities:

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency (f) = 262 Hz
- Velocity (v) = 1480 m/s

2. **Use the wave equation:**
The relationship between velocity (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \cdot \lambda \]
Here, \( \lambda \) is the wavelength we want to find.

3. **Rearrange the formula to solve for wavelength (λ):**
To find the wavelength, we can rearrange the formula:
\[ \lambda = \frac{v}{f} \]

4. **Substitute the known values into the equation:**
Now, substitute the values of velocity and frequency into the rearranged formula:
\[ \lambda = \frac{1480 \, \text{m/s}}{262 \, \text{Hz}} \]

5. **Calculate the wavelength:**
Performing the division:
\[ \lambda = \frac{1480}{262} \approx 5.645 \, \text{m} \]

6. **Round the answer:**
Rounding to two decimal places, we get:
\[ \lambda \approx 5.64 \, \text{m} \]

### Final Answer:
The wavelength of the wave is approximately **5.64 meters**.

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