An observer standing near the sea-coast counts 48 waves per min. If the wavelength of the wave is 10 m, the velocity of the waves will be

Options

A. 8 m/s
B. 12 m/s
C. 16 m/s
D. 20 m/s

Explanation

To solve the problem, we need to find the velocity of the waves given the frequency and wavelength. Let's break it down step by step.

### Step-by-Step Solution:

1. **Determine the Frequency**:
The observer counts 48 waves per minute. To find the frequency in Hertz (Hz), we convert this to waves per second.
\[ \text{Frequency} (f) = \frac{\text{Number of waves}}{\text{Time in seconds}} = \frac{48 \text{ waves}}{60 \text{ seconds}} = 0.8 \text{ Hz} \]

2. **Identify the Wavelength**:
The problem states that the wavelength (λ) of the wave is 10 meters.
\[ \text{Wavelength} (\lambda) = 10 \text{ m} \]

3. **Use the Wave Velocity Formula**:
The velocity (v) of a wave can be calculated using the formula:
\[ v = \lambda \times f \]

4. **Substitute the Values**:
Now, we substitute the values of wavelength and frequency into the formula.
\[ v = 10 \text{ m} \times 0.8 \text{ Hz} = 8 \text{ m/s} \]

5. **Conclusion**:
Therefore, the velocity of the waves is:
\[ v = 8 \text{ m/s} \]

### Final Answer:
The velocity of the waves is **8 m/s**.

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