Sound waves from a tuning fork `A` reacha point `P` by two separate paths `ABP` and `ACP`. When `ACP` is greater than `ABP` by `11.5 cm`, there is silence at `p`. When the difference is `23 cm` the sound becomes loudest at `P` and `34.5 cm` there is silence again and so on. Calculate the minimum frequency of the fork if the velocity of sound is taken to be `331.2 m//s`.

Explanation

To solve the problem, we need to analyze the conditions given for the sound waves reaching point P from the tuning fork A via two different paths: ABP and ACP.

### Step-by-Step Solution:

1. **Understanding the Conditions**:
- When the path difference \( ACP - ABP = 11.5 \, \text{cm} \), there is silence at point P. This indicates that the waves are out of phase, leading to destructive interference.
- When the path difference is \( 23 \, \text{cm} \), the sound is loudest at P, indicating constructive interference.
- When the path difference is \( 34.5 \, \text{cm} \), there is silence again, indicating destructive interference.
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