In a resonance tube, the first resonance is obtained when the level of water in the tube is at 16 cm from the open end. Neglecting end correction, the next resonance will be obtained when the level of water from the open end is

Options

A. `24 cm`
B. `32 cm`
C. `48 cm`
D. `64 cm`

Answer

To solve the problem of finding the level of water in a resonance tube at which the next resonance occurs, we can follow these steps:

### Step 1: Understand the concept of resonance in a tube
In a resonance tube, resonance occurs when the length of the air column supports standing waves. The first resonance occurs when the length of the air column is equal to \( \frac{1}{4} \lambda \) (where \( \lambda \) is the wavelength of the sound wave).

### Step 2: Identify the first resonance condition
Given that the first resonance is obtained when the water level is at 16 cm from the open end, this means that the length of the air column is:
\[ L_1 = 16 \, \text{cm} \]

### Step 3: Determine the condition for the next resonance
For the next resonance, the length of the air column will be:
\[ L_2 = \frac{3}{4} \lambda \]
This means that the second resonance occurs when the length of the air column increases to \( \frac{3}{4} \) of the wavelength.

### Step 4: Calculate the length of the air column for the second resonance
The relationship between the first and second resonance can be established as follows:
- The first resonance corresponds to \( \frac{1}{4} \lambda \) (16 cm).
- The second resonance corresponds to \( \frac{3}{4} \lambda \).

From the first resonance, we can find \( \lambda \):
\[ L_1 = \frac{1}{4} \lambda \]
\[ \lambda = 4 \times L_1 = 4 \times 16 \, \text{cm} = 64 \, \text{cm} \]

Now, we can find the length of the air column for the second resonance:
\[ L_2 = \frac{3}{4} \lambda = \frac{3}{4} \times 64 \, \text{cm} = 48 \, \text{cm} \]

### Step 5: Determine the water level for the second resonance
Since the length of the air column at the second resonance is 48 cm, the water level from the open end will be:
\[ \text{Water level} = \text{Total length of tube} - L_2 \]
Assuming the total length of the tube remains constant, the water level will be:
\[ \text{Water level} = 64 \, \text{cm} - 48 \, \text{cm} = 16 \, \text{cm} \]

### Conclusion
The next resonance will be obtained when the level of water from the open end is:
\[ 48 \, \text{cm} \]