Length of a string tied to two rigid support is `40cm`. Maximum length (wavelength in cm) of a stationary wave produced on it is

Options

A. 20
B. 80
C. 40
D. 120

Explanation

To solve the problem of finding the maximum wavelength of a stationary wave produced on a string tied to two rigid supports, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**: The string is tied between two rigid supports, creating a fixed length. The length of the string (L) is given as 40 cm.

2. **Identify the Wave Characteristics**: In a stationary wave, nodes and antinodes are formed. The maximum wavelength occurs when there is one antinode in the middle of the string.

3. **Determine the Relationship Between Length and Wavelength**: For a string fixed at both ends, the relationship between the length of the string (L) and the wavelength (λ) is given by:
\[ L = \frac{\lambda}{2} \]
This means that the length of the string is half of the wavelength when there is one antinode.

4. **Calculate the Wavelength**: Rearranging the formula gives us:
\[ \lambda = 2L \]
Substituting the given length of the string:
\[ \lambda = 2 \times 40 \, \text{cm} = 80 \, \text{cm} \]

5. **Conclusion**: The maximum wavelength of the stationary wave produced on the string is 80 cm.

### Final Answer:
The maximum wavelength of the stationary wave produced on the string is **80 cm**.

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