Question

The equation of a standing wave is obtained by adding the displacements of two waves traveling in opposite directions. Assume that each of the waves has amplitude A, period T, and wavelength λ. If the models for these waves are _________.

Answer 1

A standing wave is formed by the superposition of two waves moving in opposite directions. The resulting wave appears to be a sine wave with nodes at integer multiples of half wavelengths and antinodes at odd multiples of quarter wavelengths.

Step-by-step explanation:

A standing wave is formed by the superposition of two waves moving in opposite directions. When two identical sinusoidal waves, represented by y1(x, t) = A sin(kx - wt) and y2(x, t) = A sin(kx + wt), move in opposite directions, they create a standing wave.

The amplitude (A), period (T), and wavelength (λ) remain the same for both waves. The resulting wave appears to be a sine wave with nodes at integer multiples of half wavelengths and antinodes at odd multiples of quarter wavelengths. The nodes are points of no motion in standing waves.