In a stationary waves, the amplitude of vibrating paticles

Options

A. Remains constant
B. Zero
C. Varies from particle to particle
D. Maximum

Answer

**Step-by-Step Solution:**

1. **Understanding Stationary Waves**:
Stationary waves are formed by the interference of two waves traveling in opposite directions. They consist of nodes (points of no displacement) and antinodes (points of maximum displacement).

2. **Equation of Stationary Waves**:
The standard equation for a stationary wave can be expressed as:
\[ y(x, t) = 2A \sin(kx) \sin(\omega t) \]
where \( A \) is the amplitude, \( k \) is the wave number, and \( \omega \) is the angular frequency.

3. **Identifying Amplitude**:
The amplitude of the vibrating particles in a stationary wave is determined by the maximum displacement from the equilibrium position. In the equation, the term \( 2A \) represents the maximum amplitude of the wave.

4. **Behavior of Particles**:
In a stationary wave, different particles oscillate with different amplitudes depending on their position. The particles at the antinodes have the maximum amplitude, while those at the nodes have zero amplitude.

5. **Variation of Amplitude**:
The amplitude varies from particle to particle along the length of the wave. For example, the amplitude at an antinode is \( 2A \), while at a node, it is \( 0 \). Therefore, the amplitude is not constant across the wave.

6. **Conclusion**:
The amplitude of vibrating particles in a stationary wave varies from particle to particle, depending on their position relative to the nodes and antinodes.

**Final Answer**: The amplitude of vibrating particles in a stationary wave varies from particle to particle.

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