The end correction of a resonance tube is `1 cm`. If shortest resonating length is `15 cm`, the next resonating length will be.

Options

A. (a)47 cm
B. (b)45 cm
C. (c)50 cm
D. (d)33 cm

Explanation

To find the next resonating length in a resonance tube, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- End correction (e) = 1 cm
- Shortest resonating length (L1) = 15 cm

2. **Understand the Formula**:
The formula for the next resonating length (L2) in terms of the first resonating length (L1) and the end correction (e) is:
\[ L2 = 2e + 3L1 \]

3. **Substitute the Values**:
Substitute the given values into the formula:
\[ L2 = 2 \times 1 \, \text{cm} + 3 \times 15 \, \text{cm} \]

4. **Calculate Each Part**:
- Calculate \(2 \times 1 \, \text{cm} = 2 \, \text{cm}\)
- Calculate \(3 \times 15 \, \text{cm} = 45 \, \text{cm}\)

5. **Add the Results**:
Now, add the two results together:
\[ L2 = 2 \, \text{cm} + 45 \, \text{cm} = 47 \, \text{cm} \]

6. **Conclusion**:
The next resonating length (L2) is 47 cm.

### Final Answer:
The next resonating length will be **47 cm**.

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