Question

The number of waves counted by an observer on the sea-coast in one minute is 54. If the wavelength of the waves is \(5 \text{m}\) then the velocity of the waves in \(\text{m/s}\) will be

• A. \(4.5\)
• B. \(5.4\)
• C. \(6.3\)
• D. \(7.2\)

Hint:

Wave speed is frequency times wavelength.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The speed of a wave is \(v = f\lambda\), where \(f\) is the number of waves passing a point each second.

Step 2: Key Formula or Approach:
\(54\) waves are counted in one minute, which is \(60\) s.

Step 3: Detailed Explanation:
\(f = \frac{54}{60} = 0.9\) Hz.
\[ v = f\lambda = 0.9 \times 5 = 4.5\ \text{m/s} \]
The wavelength is in metres and the frequency is in hertz, so the product comes out directly in m/s. Check by distance: \(54 \times 5 = 270\) m of wave pattern passes in \(60\) s, which is \(4.5\) m each second.

Final Answer:
The wave speed is \(4.5\) m/s, option (A). \[ \boxed{4.5\ \text{m/s}} \]