In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.17 sec. The frequency of the wave is

Options

A. 1.47 Hz
B. 0.36 Hz
C. 0.73 Hz
D. 2.94 Hz

Explanation

To find the frequency of the sinusoidal wave given that the time required for a particular point to move from maximum displacement to zero displacement is 0.17 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion**: In a sinusoidal wave, the motion of a particle can be described in terms of its displacement over time. The maximum displacement (amplitude) occurs at the peak of the wave, and the zero displacement occurs at the equilibrium position.

2. **Identifying the Time Interval**: The time taken for a particle to move from maximum displacement (amplitude) to zero displacement is given as 0.17 seconds. This movement corresponds to one-quarter of the wave's period (T), as the particle moves from the peak to the equilibrium position.

3. **Relating Time to Period**: Since the time taken to move from maximum displacement to zero is \( T/4 \), we can set up the equation:
\[ \frac{T}{4} = 0.17 \text{ seconds} \]

4. **Calculating the Period (T)**: To find the total period (T), we multiply both sides of the equation by 4:
\[ T = 0.17 \times 4 = 0.68 \text{ seconds} \]

5. **Finding the Frequency (f)**: The frequency (f) of a wave is the reciprocal of the period (T). Thus, we can calculate the frequency as follows:
\[ f = \frac{1}{T} = \frac{1}{0.68} \]

6. **Calculating the Frequency**: Performing the calculation gives:
\[ f \approx 1.47 \text{ Hz} \]

### Final Answer:
The frequency of the wave is approximately **1.47 Hz**.

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