Distance between trough and crest of waves is 1.5m while distance between two trough is 5m. Which of following wavelength is possible

Options

A. `1/2, 1/4, 1/6, .....`
B. `1,2,3,....`
C. `1/1, 1/3, 1/5,....`
D. `1,3,5,....`

Answer

To solve the problem, we need to analyze the information given about the waves and derive the possible wavelength.

### Step-by-Step Solution:

1. **Understanding the Terms**:
- The distance between a trough and a crest is given as 1.5 m.
- The distance between two troughs is given as 5 m.

2. **Relating Distances to Wavelength**:
- The distance between a trough and a crest is half of the wavelength (λ/2). Therefore, we can write:
\[ \frac{\lambda}{2} = 1.5 \, \text{m} \]
- From this, we can find the wavelength:
\[ \lambda = 2 \times 1.5 = 3 \, \text{m} \]

3. **Distance Between Troughs**:
- The distance between two troughs is equal to the wavelength (λ). Given that the distance between two troughs is 5 m, we can write:
\[ \lambda = 5 \, \text{m} \]

4. **Finding Possible Wavelengths**:
- We have two equations for the wavelength:
- From the first relation, we found λ = 3 m.
- From the second relation, we found λ = 5 m.
- Since the distance between two troughs (5 m) is greater than the distance between a trough and a crest (1.5 m), we can conclude that the possible wavelengths must satisfy both conditions.

5. **Conclusion**:
- The possible wavelengths that satisfy the conditions given in the problem are:
- λ = 3 m (from the distance between trough and crest)
- λ = 5 m (from the distance between two troughs)
- Since the question asks for which of the following wavelengths is possible, we conclude that both 3 m and 5 m are valid wavelengths.