The end correction of a resonance column in resonance tube experiment is `0.5` cm. If the shortest length resonating with a tuning fork is 16 cm, then the next resonating length will be

Options

A. 49 cm
B. 39 cm
C. 32 cm
D. 55 cm

Explanation

To solve the problem step by step, we will use the concept of end correction in a resonance tube experiment.

### Step 1: Understand the Given Information
We are given:
- End correction (E) = 0.5 cm
- Shortest resonating length (L1) = 16 cm

### Step 2: Use the Formula for End Correction
The formula for end correction in a resonance tube is given by:
\[ E = \frac{L2 - 3L1}{2} \]
where:
- L2 is the next resonating length we need to find.
- L1 is the shortest resonating length.

### Step 3: Substitute the Known Values
Substituting the known values into the formula:
\[ 0.5 = \frac{L2 - 3 \times 16}{2} \]

### Step 4: Simplify the Equation
First, multiply both sides by 2 to eliminate the fraction:
\[ 1 = L2 - 48 \]

### Step 5: Solve for L2
Now, add 48 to both sides to isolate L2:
\[ L2 = 1 + 48 \]
\[ L2 = 49 \text{ cm} \]

### Conclusion
The next resonating length (L2) will be **49 cm**.

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