Question

Two waves of same frequency (\(n\)) approaching each other with same velocity of \(18\) m/s interfere. The distance between two consecutive antinodes is

• A. \(\frac{18}{n}\)
• B. \(\frac{10}{n}\)
• C. \(\frac{9}{n}\)
• D. \(\frac{n}{18}\)

Hint:

The wavelength is velocity over frequency, and consecutive antinodes are half a wavelength apart.

Answer 1

The Correct Option is C

Step 1: Understand the concept
Two identical waves travelling in opposite directions form a stationary wave. The distance between two consecutive antinodes is \(\dfrac{\lambda}{2}\).

Step 2: Find the wavelength
The wave speed is \(v = 18\) m/s and the frequency is \(n\), so \(\lambda = \dfrac{v}{n} = \dfrac{18}{n}\) m.

Step 3: Compute
\[ \text{distance} = \frac{\lambda}{2} = \frac{9}{n}\ \text{m} \]

Step 4: Result
Option (C). The value \(\frac{18}{n}\) is the full wavelength, which is the distance between alternate antinodes, not consecutive ones.

Final Answer:
Consecutive antinodes are 9/n metres apart. This is option (C). \[ \boxed{\text{(C) }\frac{9}{n}} \]