Let the frequencies of tuning fork and piano string be υ1 and υ2 respectively. ∴υ2=υ1±4=512Hz±4=516Hz or 508Hz
Increase in the tension of a piano string increases its frequency. If υ2=516Hz, further increase in υ2, resulted in an increase in the beat frequency. But this is not given in the question. If υ2=508Hz, further increase in υ2 resulted in decrease in the beat frequency. This is given in the question. When the beat frequency decreases to 2 beats per second. Therefore, the frequency of the piano string before increasing the tension was 508Hz.