To find the wavelength from two non-adjacent nodes on a stationary wave, count the gaps between the nodes. Every gap between adjacent nodes is half a wavelength. Divide the measured distance by the number of gaps, then double the result.
This H2 Physics 9478 practice uses a stationary wave on a string to connect the pattern you see with the wavelength used in the wave equation.
- Mark all nodes between the two reference points.
- Count the intervals between nodes.
- Double the distance per interval to find wavelength.
- Use that wavelength with the given frequency to calculate wave speed.
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Count intervals on the string
Nodes are points where the displacement remains zero in the ideal stationary-wave pattern. In the familiar pattern on a stretched string, each segment between adjacent nodes contains one antinode and spans half a wavelength.
If you include both endpoints when you count nodes, the number of gaps is one fewer than the number of nodes. Five nodes in a row give four gaps. Measuring over several gaps can also reduce the fractional effect of a fixed reading uncertainty, provided the endpoints are clearly identified.
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Worked example | Five nodes across 0.80 m
The first and fifth nodes on a string are 0.80 m apart. Four gaps fit into this distance, so adjacent nodes are 0.80 ÷ 4 = 0.20 m apart. The wavelength is 2 × 0.20 = 0.40 m.
If the driver frequency is 75 Hz, the speed of the travelling waves that form the stationary wave is 75 × 0.40 = 30 m s⁻¹. The nodes remain in place even though the underlying waves travel along the string.
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Change one reference point
Take the first node and the antinode in the third gap. There are two full gaps followed by half of the third gap. In the same pattern that is 0.20 + 0.20 + 0.10 = 0.50 m. In wavelength terms it is λ/2 + λ/2 + λ/4 = 5λ/4, again giving λ = 0.40 m.
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Frequently asked questions
Is every point with zero displacement a node?
A node stays at zero throughout the oscillation. At an instant when the entire string passes through its equilibrium position, points away from the nodes also have zero displacement.
Can I use two antinodes instead?
Yes. Adjacent antinodes are also half a wavelength apart. Count the intervals if the two antinodes are separated by others.