Demonstrating Stationary Waves

Stationary waves can be demonstrated, and used to measure wavelength, with microwaves or sound.Microwaves: a microwave transmitter faces a flat metal plate, which reflects the microwaves straight back. The incident and reflected waves superpose to form a stationary wave between the transmitter and the plate. A microwave probe (detector) connected to a meter is moved slowly along the line between them. The reading rises and falls: it is a minimum at each node and a maximum at each antinode.Sound: a loudspeaker driven by a signal generator faces a hard reflecting board. A small microphone connected to an oscilloscope is moved between them. The trace amplitude falls at nodes and rises at antinodes.Adjacent nodes are half a wavelength apart. To reduce the percentage uncertainty, measure the distance across many nodes and divide by the number of node spacings, rather than measuring one gap.Worked example: a microwave probe passes through 7 nodes, and the distance from the first to the seventh is 9.0 cm. That is 6 node spacings, so λ/2 = 9.0 / 6 = 1.5 cm and λ = 3.0 cm. Microwaves travel at 3.0 × 10⁸ m s^-1, so the frequency is f = v/λ = 3.0 × 10⁸ / 0.030 = 1.0 × 10¹⁰ Hz, which is 10 GHz.The minima are not completely zero near the transmitter, because the reflected wave has spread out and is weaker than the incident wave, so the cancellation is not complete.