Physics · Wave behaviour. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A standing wave forms when two waves of the same frequency and amplitude travel in opposite directions and superpose, for example a wave and its reflection. The pattern does not move along, and no energy is transferred along the medium.
At nodes the displacement is always zero. At antinodes the amplitude is greatest. All points between two adjacent nodes move in phase, but with different amplitudes. Points on opposite sides of a node are in antiphase.
Only certain wavelengths fit the boundaries, and these give the harmonics. Every system also has a natural frequency. If a driver forces it at that frequency, the amplitude becomes large: this is resonance. Damping removes energy and reduces the amplitude.
Students give a pipe closed at one end all the harmonics. It has only the odd ones, so its allowed frequencies are 1, 3, 5, ... times the first harmonic, and its first harmonic uses λ = 4L, not 2L.
Answer: 180 m s−1
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