state whether the variation pressure at nodes in a stationary wave is maximum or zero .justify
In a stationary wave, the variations in pressure at different nodes can be described as a result of constructive and destructive interference between two waves that are travelling in opposite directions.
To determine whether the variation in pressure at nodes is maximum or zero, let's consider a simplified representation of a stationary wave. Imagine a string that is fixed at both ends and undergoing harmonic oscillations. As the waves propagate through the string, they reflect from the fixed boundaries, resulting in a stationary wave pattern.
In a stationary wave, there are regions where the string remains stationary called nodes, and other regions where the string oscillates with maximum amplitude called antinodes.
At nodes, the two waves interfere destructively. This means that the crest of one wave aligns with the trough of the other wave, resulting in a cancelation of their displacements. Since pressure in a medium is related to the displacement of particles, at nodes, the variations in pressure are minimum or zero.
On the other hand, at antinodes, the two waves interfere constructively. The crest of one wave aligns with the crest of the other wave, and the troughs align as well. This results in amplification of their displacements and subsequent amplification of pressure variations. Therefore, at antinodes, the variations in pressure are maximum.
To summarize, in a stationary wave, the variation in pressure at nodes is minimum or zero (sometimes called nodes of zero pressure), while the variation in pressure at antinodes is maximum.