Given data

• Frequency of tuning fork: $f = 250\,\text{Hz}$
• Speed of sound in air: $v = 340\,\text{m s}^{-1}$

Find the wavelength Using $v = f\lambda$ so, $\lambda = \frac{v}{f} = \frac{340}{250} = 1.36\,\text{m}$

Condition for resonance in a closed organ pipe For a closed organ pipe, resonant lengths are: $L = \frac{\lambda}{4},\ \frac{3\lambda}{4},\ \frac{5\lambda}{4}, \dots$ The shortest length is: $L = \frac{\lambda}{4} = \frac{1.36}{4} = 0.34\,\text{m}$

Convert into cm $0.34\,\text{m} = 34\,\text{cm}$

Final answer The length of the shortest closed organ pipe is: $\boxed{34\,\text{cm}}$