The distance between consecutive crest and trough of a wave is `10 cm`. If the speed of wave is `200 cm/s`. Then the time period of wave is

Options

A. 0.01 s
B. 0.2 s
C. 0.02 s
D. 0.1

Answer

To find the time period of the wave, we can follow these steps:

### Step 1: Understand the given information
We are given:
- Distance between consecutive crest and trough (d) = 10 cm
- Speed of the wave (v) = 200 cm/s

### Step 2: Determine the wavelength
The distance between a crest and the next trough is half of the wavelength. Therefore, the wavelength (λ) can be calculated as:
\[ \lambda = 2 \times d = 2 \times 10 \text{ cm} = 20 \text{ cm} \]

### Step 3: Use the wave speed formula
The speed of a wave is related to its frequency (f) and wavelength (λ) by the formula:
\[ v = f \cdot \lambda \]
We can rearrange this formula to express frequency in terms of speed and wavelength:
\[ f = \frac{v}{\lambda} \]

### Step 4: Calculate the frequency
Substituting the known values into the frequency formula:
\[ f = \frac{200 \text{ cm/s}}{20 \text{ cm}} = 10 \text{ Hz} \]

### Step 5: Relate frequency to time period
The time period (T) is the reciprocal of frequency:
\[ T = \frac{1}{f} \]

### Step 6: Calculate the time period
Substituting the frequency we found:
\[ T = \frac{1}{10 \text{ Hz}} = 0.1 \text{ s} \]

### Final Answer
The time period of the wave is \(0.1\) seconds.

---