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
Show Hint
In a stationary wave:
\[
\text{node-to-node distance}=\frac{\lambda}{2}
\]
and
\[
\lambda=\frac{v}{f}
\]
Step 1: Understanding the Concept:
When two identical waves travel in opposite directions and interfere, they produce a stationary (standing) wave. Nodes are points where the amplitude is always zero. Step 2: Key Formula or Approach:
1. Wave velocity: $v = n \lambda$
2. Distance between consecutive nodes: $d = \frac{\lambda}{2}$ Step 3: Detailed Explanation:
Given $v = 12\text{ m/s}$ and frequency $= n$.
1. Find the wavelength $\lambda$:
\[ \lambda = \frac{v}{n} = \frac{12}{n} \]
2. The distance between two consecutive nodes in a standing wave is exactly half a wavelength:
\[ \text{Distance} = \frac{\lambda}{2} = \frac{12/n}{2} = \frac{6}{n} \] Step 4: Final Answer:
The distance is $\frac{6}{n}$.