1. Resonance column relation

For a resonance column experiment with one end closed, resonance occurs at

$L_n=(2n-1)\frac{\lambda}{4}, \quad n=1,2,3,\dots$

So:

• First resonance: $L_1=\frac{\lambda}{4}$
• Second resonance: $L_2=\frac{3\lambda}{4}$

2. Winter observation

The first resonance length in winter is given as

$L_1=18\text{ cm}$

Hence winter wavelength is

$\lambda_w=4\times 18=72\text{ cm}$

3. Effect of summer

Speed of sound in air increases in summer because temperature is higher.

Using

$v=f\lambda$

and noting that the tuning fork frequency $f$ remains constant, a larger speed means a larger wavelength in summer:

$\lambda_s>\lambda_w=72\text{ cm}$

4. Second resonance in summer

For second resonance in summer,

$x=L_2=\frac{3\lambda_s}{4}$

Since $\lambda_s>72$ cm,

$x>\frac{3\times 72}{4}=54\text{ cm}$

Thus,

$x>54$

5. Checking options

• A: $18>x$ → false
• B: $x>54$ → true
• C: $54>x>36$ → false
• D: $36>x>18$ → false

Therefore, the correct option is B.