An observer standing at the sea coast observes `54 waves` reaching the coast per minute. If the wavelength of a wave is `10 m`, find the wave velocity.

Options

A. `19 m//sec`
B. `29 m//sec`
C. `9 m//sec`
D. `39 m//sec`

Answer

To find the wave velocity, we can follow these steps:

### Step 1: Determine the frequency of the waves
The observer sees 54 waves reaching the coast per minute. To find the frequency (f) in Hertz (Hz), we need to convert minutes to seconds.

\[ f = \frac{54 \text{ waves}}{1 \text{ minute}} = \frac{54 \text{ waves}}{60 \text{ seconds}} = 0.9 \text{ Hz} \]

### Step 2: Use the wavelength
The wavelength (λ) of the wave is given as 10 meters.

### Step 3: Calculate the wave velocity
The wave velocity (v) can be calculated using the formula:

\[ v = f \times \lambda \]

Substituting the values we have:

\[ v = 0.9 \text{ Hz} \times 10 \text{ m} = 9 \text{ m/s} \]

### Final Answer
The wave velocity is 9 m/s.

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