Standing Wave Nodes

Question

Distance between adjacent nodes in standing wave equals?

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1. **Standing Waves**: Formed by the superposition of two waves of same frequency and amplitude traveling in opposite directions: $y = (2A \sin kx) \cos \omega t$.
2. **Nodes**: Points in the medium that remain permanently at rest. These occur where $\sin kx = 0$.
3. **Positions**: $kx = n\pi = 0, \pi, 2\pi, \dots$.
   - Since $k = 2\pi/\lambda$, then $x = n \frac{\lambda}{2} = 0, \frac{\lambda}{2}, \lambda, \dots$.
4. **Spacing**: The distance between consecutive nodes is the difference between these positions:
   - Displacement $= \frac{\lambda}{2} - 0 = \frac{\lambda}{2}$.
5. **Conclusion**: Nodes are spaced at intervals of **$λ/2$**. The same applies to the spacing between adjacent antinodes.

Standing Wave Nodes

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