The speed of wave in a certain medium is `100m/s`. If 1000 waves pass over a certain point of the medium in 1 minute 40 second, the wavelength is

Options

A. 2m
B. 4m
C. 8m
D. 10m

Answer

To find the wavelength of the wave in the given medium, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Speed of the wave (v) = 100 m/s
- Number of waves (N) = 1000
- Time (t) = 1 minute 40 seconds

2. **Convert Time to Seconds**:
- 1 minute = 60 seconds
- Therefore, 1 minute 40 seconds = 60 seconds + 40 seconds = 100 seconds.

3. **Calculate Frequency (f)**:
- Frequency is defined as the number of waves passing a point in one second.
- We have 1000 waves passing in 100 seconds.
- To find the frequency, we can use the formula:
\[ f = \frac{N}{t} \]
- Substituting the values:
\[ f = \frac{1000 \text{ waves}}{100 \text{ seconds}} = 10 \text{ Hz} \]

4. **Use the Wave Equation to Find Wavelength (λ)**:
- The relationship between speed (v), frequency (f), and wavelength (λ) is given by:
\[ v = f \cdot \lambda \]
- Rearranging this formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]
- Substituting the known values:
\[ \lambda = \frac{100 \text{ m/s}}{10 \text{ Hz}} = 10 \text{ m} \]

5. **Conclusion**:
- The wavelength (λ) of the wave in the medium is **10 meters**.