1. 11: Wave Phenomena 11.1 Standing (Stationary) Waves

2. Standing (Stationary) Waves When two identical travelling waves pass in the opposite direction through a medium, a stationary wave may be produced. In this situation there is zero net transfer of energy through the medium. Demo: Stationary waves on a rubber cord: Vibration generator Pulley

4. Formation of Standing Waves Standing waves form as a result of constructive and destructive superposition of two waves moving in opposite directions with equal amplitude and frequency. If at an instant when the waves overlap any points are in-phase, constructive superposition occurs. - diagram If each wave moves ¼ of a cycle in opposite directions, the waves become ½ a cycle out of phase and destructive interference occurs. - diagram

5. Nodes and Antinodes Points oscillating with the biggest amplitude in a stationary wave are called antinodes. Points undergoing zero oscillation are called nodes.

6. Harmonic Frequencies For any stationary wave the node to node distance = ½ λ So for waves on a string, a stationary wave will only occur when the length is a whole number of half wavelengths. Thus, because the speed of the wave in the string is fixed (depending on the string and its tension), a stationary wave pattern can only be formed at certain frequencies – ‘harmonics’.

7. λ = 2L Frequency = f λ = L Frequency = 2f λ = 2/3 L Frequency = 3f

8. The lowest resonant frequency of the system is called the fundamental frequency (or 1 st harmonic frequency). The next are called the 2 nd harmonic, 3 rd harmonic etc. For a stationary wave in a string: Harmonic frequency = no. of loops x natural frequency

9. Comparing Standing Waves to Progressive Waves Progressive WavesStanding Waves Wave profile progresses (moves) Wave profile doesn’t progress (stays still) All points oscillate with the same amplitude Amplitude varies from zero (node) to maximum (antinode) All points are out of phase with each other All points between any two nodes oscillate in phase with each other

10. Standing Waves in Pipes Wind instruments often use

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