In a stationary longitudinal wave, nodes are points of

Options

A. minimum displacement and minimum pressure change.
B. minimum displacement and maximum pressure change
C. maximum displacement and maximum pressure change
D. maximum displacement and minimum pressure change.

Explanation

To solve the question regarding the characteristics of nodes in a stationary longitudinal wave, let's break it down step by step.

### Step 1: Understand the Concept of Longitudinal Waves
In a longitudinal wave, particles of the medium move parallel to the direction of wave propagation. This results in areas of compression (where particles are close together) and rarefaction (where particles are spread apart).

**Hint:** Remember that in longitudinal waves, the motion of the medium's particles is along the same direction as the wave travels.

### Step 2: Define Nodes in Stationary Waves
In stationary waves, nodes are points where the amplitude of the wave is always zero. This means that at these points, the particles of the medium do not move; they remain at their equilibrium position.

**Hint:** Nodes are characterized by zero displacement of particles.

### Step 3: Analyze Pressure Changes at Nodes
At the nodes of a longitudinal wave, since the particles do not move, there is no displacement. However, the pressure at these points is also affected. In a stationary longitudinal wave, nodes correspond to points of minimum pressure change. This is because at nodes, the compressions and rarefactions are balanced, resulting in no net change in pressure.

**Hint:** Consider how compressions and rarefactions interact at the nodes.

### Step 4: Conclusion
Thus, in a stationary longitudinal wave, nodes are points of minimum displacement and minimum pressure change.

**Final Answer:** Nodes are points of minimum displacement and minimum pressure change.