Final answer:
The frequency of tuning fork A before filing was 316 Hz, as filing a tuning fork typically increases its frequency. Tuning fork A thus initially produced 4 beats per second with tuning fork B of 320 Hz either by having a frequency of 316 Hz or 324 Hz, but filing confirms the lower frequency.
Step-by-step explanation:
When a tuning fork A with an unknown frequency produces 4 beats per second with tuning fork B, which has a frequency of 320 Hz, there are two possible frequencies for A. It could be 4 Hz more or 4 Hz less than the frequency of B. Therefore, the two possibilities for the frequency of fork A are 320 Hz + 4 Hz = 324 Hz or 320 Hz - 4 Hz = 316 Hz.
However, after filing one of the prongs of tuning fork A, 4 beats per second are heard again, which means the frequency of A has changed. Filing usually increases the frequency of the tuning fork since it removes material and decreases mass, making it vibrate faster. Therefore, the frequency of fork A before filing was 316 Hz, as filing would have increased its frequency to match the 320 Hz of fork B producing the same beat frequency.