Question

1. explain the phenomenon of a standing wave. sketch a picture and clearly mark a node.

Explanation:

A standing wave is formed when two waves of the same frequency, amplitude, and wavelength travel in opposite directions (e.g., an incident wave and its reflection) and interfere. At nodes, the displacement is always zero due to destructive interference (the waves cancel each other here). For the sketch: Draw a coordinate system with the x - axis as the medium (like a string) and the y - axis as displacement. The standing wave has points (nodes) where y = 0 at all times, and antinodes (maximum displacement) between them. Mark a node as a point on the x - axis (where the wave crosses the axis) with a label like "Node" at that point.

Answer:

• Explanation of Standing Wave: A standing wave is produced by the superposition (interference) of two sinusoidal waves with the same frequency, amplitude, and wavelength that propagate in opposite directions through the same medium. For example, when a wave travels along a string fixed at both ends, the incident wave reflects from the ends, and the incident and reflected waves interfere. In this interference, some points (nodes) have zero displacement at all times (due to destructive interference, where the displacements of the two waves at that point are equal in magnitude and opposite in direction), while other points (antinodes) have maximum displacement (due to constructive interference, where the displacements add up).
• Sketch Description (Text - based):
• Draw a horizontal line (representing the equilibrium position of the medium, e.g., a string) along the x - axis.
• Draw a sinusoidal - like curve (the standing wave) that oscillates above and below the x - axis. The points where the curve intersects the x - axis are nodes (mark one such point with the label "Node"). Between two nodes, the curve reaches maximum heights (antinodes) above and below the x - axis.

(Note: For a graphical sketch, on paper, you can draw a string - like horizontal line, then draw the standing wave as a wave with fixed nodes (e.g., at the ends and at regular intervals in between for a string fixed at both ends) and moving antinodes, but the node positions remain stationary.)