In a sinusoidal wave, the time required by a particular particle to move from maximum displacement to zero displacement is 0.025 sec. The frequency of the wave is

Options

A. 2.5 Hz
B. 5 Hz
C. 7.5 Hz
D. 10 Hz

Explanation

To find the frequency of the sinusoidal wave given the time it takes for a particle to move from maximum displacement to zero displacement, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion of the Particle**:
- In a sinusoidal wave, a particle moves from maximum displacement (amplitude) to zero displacement (equilibrium position). This motion corresponds to a quarter of a complete cycle of the wave.

2. **Identify the Time Given**:
- The time taken for the particle to move from maximum displacement to zero displacement is given as \( t = 0.025 \) seconds.

3. **Relate Time to the Wave Period**:
- Since moving from maximum displacement to zero displacement represents a quarter of the wave's period \( T \), we can express this relationship mathematically:
\[ t = \frac{T}{4} \]

4. **Calculate the Wave Period \( T \)**:
- Rearranging the equation gives:
\[ T = 4t = 4 \times 0.025 \, \text{s} = 0.1 \, \text{s} \]

5. **Calculate the Frequency \( f \)**:
- Frequency \( f \) is the reciprocal of the period \( T \):
\[ f = \frac{1}{T} = \frac{1}{0.1 \, \text{s}} = 10 \, \text{Hz} \]

### Final Answer:
The frequency of the wave is \( 10 \, \text{Hz} \).

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