Question

QC Two waves simultaneously present on a long string have a phase difference π between them so that a standing wave formed from their combination is described by
y(x,t) = 2Asin( kx + π/2 ) cos( ωt - π/2) (a) Despite the presence of the phase angle π, is it still true that the nodes are one-half wavelength apart? Explain.

Answer 1

The equation of motion of the standing wave, y(x, t) = 2•A•sin(k•x + π/2)•cos(w•t - π/2), indicates that it is still true that the nodes are one half the wavelength apart

Therefore;

• It is still true that the nodes are one half the wavelength apart

What are the nature of standing wave?

The equation describing the standing wave formed by the two waves is y(x, t) = 2•A•sin(k•x + π/2)•cos(w•t - π/2)

A standing wave is formed when two waves that have equal amplitude and frequency and moving in opposite directions, are combined.

A standing wave can be formed by a wave and its reflection, resulting in a wave where there is no propagation of particles beyond the vibration region.

The fundamental frequency of a standing wave consists of two nodes and an antinode.

The wavelength is the distance between two peaks of one wave, such that two nodes are formed within the span of a wavelength, which makes the distance between nodes being half the wavelength of the wave.

Therefore;

It is still true that the nodes are one half the wavelength apart.

Learn more about standing waves in physics here:

brainly.com/question/15517720

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