Along the straight line joining two consecutive displacement nodes in a pure stationary sound wave at different points

Options

A. the S.H.M's will be in different phases
B. Velocities are in phase
C. the accelerations are in phase
D. frequencies are equal

Answer

To solve the question regarding the behavior of particles along the straight line joining two consecutive displacement nodes in a pure stationary sound wave, we can break it down into the following steps:

### Step-by-Step Solution

1. **Understanding Stationary Waves**:
- In a stationary wave, there are points called nodes where there is no displacement of particles. Between these nodes, there are points called anti-nodes where the displacement is maximum.

**Hint**: Remember that nodes are points of zero displacement, while anti-nodes are points of maximum displacement.

2. **Identifying Nodes and Anti-nodes**:
- For a stationary sound wave, nodes occur at regular intervals along the wave. The distance between two consecutive nodes is half the wavelength (λ/2).

**Hint**: Visualize the wave to identify where nodes and anti-nodes are located.

3. **Particle Motion Between Nodes**:
- The particles between two consecutive nodes oscillate with varying amplitudes. The particles at the anti-nodes have maximum amplitude, while those closer to the nodes have smaller amplitudes.

**Hint**: Consider how the amplitude changes as you move from a node to an anti-node.

4. **Direction of Motion**:
- The particles on either side of a node move in opposite directions. For example, if one particle moves upward, the adjacent particle on the other side of the node moves downward.

**Hint**: Think about the symmetry of the wave and how particles interact around nodes.

5. **Velocity and Acceleration**:
- The velocities of particles at the same distance from the nodes but on opposite sides will be equal in magnitude but opposite in direction. Similarly, their accelerations will also be equal in magnitude and opposite in direction.

**Hint**: Use the concept of harmonic motion to understand how velocity and acceleration relate to displacement.

6. **Frequency Consistency**:
- All particles in the stationary wave oscillate with the same frequency, regardless of their position between nodes or anti-nodes.

**Hint**: Frequency is a property of the wave itself and remains constant throughout.

### Final Conclusion
- Along the straight line joining two consecutive displacement nodes in a pure stationary sound wave, the particles exhibit oscillatory motion with varying amplitudes, opposite directions of motion on either side of the nodes, equal velocities and accelerations in magnitude but opposite in direction, and the same frequency.