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. 47 cm
B. 45 cm
C. 50 cm
D. 33 cm

Explanation

To find the next resonating length in a resonance tube given the end correction and the shortest resonating length, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- End correction (E) = 1 cm
- Shortest resonating length (L1) = 15 cm

2. **Identify the Formula**:
The relationship between the resonating lengths and the end correction is given by:
\[ L2 = 3L1 + 2E \]
where \(L2\) is the next resonating length.

3. **Substitute the Known Values**:
Plug in the values of \(E\) and \(L1\) into the formula:
\[ L2 = 3(15 \text{ cm}) + 2(1 \text{ cm}) \]

4. **Calculate the Values**:
- First calculate \(3L1\):
\[ 3 \times 15 \text{ cm} = 45 \text{ cm} \]
- Then calculate \(2E\):
\[ 2 \times 1 \text{ cm} = 2 \text{ cm} \]
- Now add these two results together:
\[ L2 = 45 \text{ cm} + 2 \text{ cm} = 47 \text{ cm} \]

5. **Final Result**:
The next resonating length \(L2\) is:
\[ L2 = 47 \text{ cm} \]

### Summary:
The next resonating length after the shortest resonating length of 15 cm, considering an end correction of 1 cm, is 47 cm.