What is the shortest length of an air column in an open tube in which a 340.0 Hz tuning fork can produce resonance at 20.0 degC?

To find the shortest length of an air column in an open tube that resonates at a frequency of 340.0 Hz, we use the speed of sound in air at 20.0 °C, which is approximately 343 m/s. The fundamental frequency (first harmonic) in an open tube corresponds to a wavelength that is twice the length of the tube. The wavelength (λ) can be calculated using the formula ( v = f \cdot \lambda ), where ( v ) is the speed of sound and ( f ) is the frequency. Thus, ( \lambda = \frac{v}{f} = \frac{343 , \text{m/s}}{340.0 , \text{Hz}} \approx 1.01 , \text{m} ). The shortest length of the tube, corresponding to the fundamental frequency, is half the wavelength: ( L = \frac{\lambda}{2} \approx 0.505 , \text{m} ).