In a resonance column experiment , the first resonance is obtained when the level of the water in the tube is at `20 cm` from the open end . Resonance will also be obtained when the water level is at a distance of

Options

A. `40 cm` from the open end
B. `60 cm` from the open end
C. `80 cm` from the open end
D. `100 cm` from the open end

Explanation

To solve the problem, we will analyze the resonance column experiment step by step.

### Step 1: Understand the first resonance condition
In a resonance column experiment, the first resonance occurs when there is a displacement node at the open end of the tube and a pressure antinode at the water surface. The distance from the open end to the water level at the first resonance is given as 20 cm.

### Step 2: Relate the first resonance to the wavelength
The first resonance corresponds to a quarter of the wavelength (λ/4). Therefore, we can express the length of the air column (L1) at the first resonance as:
\[ L_1 = \frac{\lambda}{4} \]
Given that \( L_1 = 20 \, \text{cm} \), we can find the wavelength (λ):
\[ \frac{\lambda}{4} = 20 \, \text{cm} \]
Multiplying both sides by 4 gives:
\[ \lambda = 80 \, \text{cm} \]

### Step 3: Determine the second resonance condition
The second resonance occurs when the length of the air column corresponds to three-quarters of the wavelength (3λ/4). This can be expressed as:
\[ L_2 = \frac{3\lambda}{4} \]

### Step 4: Substitute the value of λ into the second resonance equation
Now, we can substitute the value of λ we found:
\[ L_2 = \frac{3 \times 80 \, \text{cm}}{4} \]
Calculating this gives:
\[ L_2 = \frac{240 \, \text{cm}}{4} = 60 \, \text{cm} \]

### Conclusion
The water level will also resonate when it is at a distance of 60 cm from the open end of the tube.

### Final Answer
The water level will also resonate when it is at a distance of **60 cm** from the open end.

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