Question

Two waves of same frequency ( $n$ ) are approaching each other with same velocity $12\text{ m/s}$ along the same linear path and interfere. The distance between two consecutive nodes is

• A. $12 n$
• B. $\frac{12}{n}$
• C. $6 n$
• D. $\frac{6}{n}$

Hint:

In a stationary wave: \[ \text{node-to-node distance}=\frac{\lambda}{2} \] and \[ \lambda=\frac{v}{f} \]

Answer 1

The Correct Option is D

Concept:
For standing waves, distance between two consecutive nodes is: \[ \frac{\lambda}{2} \] Also, \[ \lambda=\frac{v}{f} \] ip

Step 1: Find the wavelength.
Given: \[ v=12\text{ m/s},\qquad f=n \] So, \[ \lambda=\frac{12}{n} \] ip

Step 2: Find node-to-node distance.
\[ \text{Distance between two consecutive nodes}=\frac{\lambda}{2} \] \[ =\frac{1}{2}\cdot \frac{12}{n}=\frac{6}{n} \] ip Hence, the correct answer is:
\[ \boxed{(D)\ \frac{6}{n}} \]