In a resonance column first and second resonance are obtained at depths `22.7` cm and `70.2` cm. The third resonance will be obtained at a depth of

Options

A. 117.7 cm
B. 92.9 cm
C. 115.5 cm
D. 113.5 cm

Answer

To find the depth at which the third resonance occurs in a resonance column, we can follow these steps:

### Step 1: Identify the given data
- First resonance depth (L1) = 22.7 cm
- Second resonance depth (L2) = 70.2 cm

### Step 2: Calculate the difference between the first and second resonance depths
The difference in depth between the first and second resonance gives us the resonance length (λ/2):
\[ \text{Resonance Length} = L2 - L1 = 70.2 \, \text{cm} - 22.7 \, \text{cm} = 47.5 \, \text{cm} \]

### Step 3: Calculate the depth of the third resonance
To find the depth of the third resonance (L3), we add the resonance length to the second resonance depth:
\[ L3 = L2 + \text{Resonance Length} = 70.2 \, \text{cm} + 47.5 \, \text{cm} = 117.7 \, \text{cm} \]

### Conclusion
The third resonance will be obtained at a depth of **117.7 cm**.

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