A nodal line is

Question

A nodal line is

BlackTom AI · Accepted Answer

Nodal lines are loci where the path difference between the waves from two sources produces destructive interference. For two coherent sources S1 and S2, a point P receives waves that travel distances r1 and r2. The key quantity is the path difference Δr = r2 − r1. Destructive interference occurs when the waves arrive out of phase by π (an odd multiple of π), i.e. when the path difference satisfies

Δr = (n + 1/2) λ,  where n = 0, 1, 2, ...

This condition means the amplitude contributions cancel (minima), so all points satisfying that relation trace out nodal lines (or nodal curves) in the wave field.

Step-by-step reasoning:
1. Waves from S1 and S2 superpose; the resultant amplitude depends on their relative phase at P.
2. Relative phase φ = (2π/λ)Δr. If φ = (2m+1)π (odd multiple of π), amplitudes are equal and opposite → destructive interference.
3. Converting φ to path difference gives Δr = (2m+1)π·(λ/2π) = (m + 1/2)λ. Each integer m selects a different nodal line (m = 0 is the first nodal line).
4. Thus every point along a nodal line always satisfies the destructive condition, so the waves from the two sources always cancel there.

Why the other choices are incorrect:
- “Always interfere constructively” is the opposite of a nodal line; that describes antinodal lines where Δr = nλ.
- “The line of points an equal distance from two sources” is the perpendicular bisector; equal distance gives Δr = 0 (constructive only if sources are in phase), so it is not generally a nodal line.
- “A line with no dals” is meaningless.

Therefore the correct choice is: a line along which the waves from two sources will always interfere destructively. This matches the provided answer.

A nodal line is单项选择题

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