A vibrating tuning fork is positioned above a glass cylinder that has been filled to the top with water. The water level is then lowered at a constant rate. The first loud sound is detected when the water level is $83.5\,\text{cm}$ above the bench. The next loud sound is detected when the water level is $17.1\,\text{cm}$ above the bench. The speed of sound in air is $340\,\text{m s}^{-1}$. Calculate the frequency of the tuning fork.
- A$128\,\text{Hz}$
- B$256\,\text{Hz}$
- C$384\,\text{Hz}$
- D$512\,\text{Hz}$