Standing Waves

Question

For string fixed at both ends length L fundamental frequency has wavelength:

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For a string fixed at both ends, periodic waves reflect from the boundaries and superimpose.
1. **Boundary Condition**: Both ends ($x=0, x=L$) must be nodes (zero amplitude).
2. **Fundamental (1st Harmonic)**: This is the simplest possible pattern with only one antinode in the middle. 
3. **Calculation**: The distance between two successive nodes is $\lambda/2$. For the fundamental, this distance is equal to the string length $L$. 
   $L = \lambda / 2 \implies \lambda = 2L$.

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Standing Waves

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