Read Standing Waves: Separate the Spatial Factor
Two equal waves travelling in opposite directions form a standing wave, even when one starts with an extra phase. Convert their sum before locating nodes.
Standing-Wave Nodes with Initial Phase is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
Use the sum-to-product identity to isolate the factor depending only on x. Set that spatial cosine or sine factor to zero, then select the smallest positive x.
Build the governing relation
Convert the answer from metres to centimetres only after choosing the nearest allowed node; the phase offset shifts all nodes together.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
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- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Setting each travelling wave to zero separately is not the node condition for their superposition.
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