A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Suppose nP = frequency of piano = ?  (nP∝T)nf = Frequency of tuning fork = 256 Hzx = Beat frequency = 5 bps, which is decreasing (5→2) after clanging the tension of piano wire Also, tension of piano wire is increasing so nP↓Hence nP↑– nf = x↓      →       Wrong           nf – nP↑= x↓       →      Correct ⇒ nP = nf – x = 256 – 5 Hz.