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
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Suppose $n_{p} =$ frequency of piano = ? $\left(n_{P} \propto \sqrt{T}\right)$
$n_{f} =$ Frequency of tuning fork = 256 Hz
x = Beat frequency = 5 bps, which is decreasing (5 → → 2) after clanging the tension of piano wire
Also, tension of piano wire is increasing so $n_{p\downarrow}$
Hence n P – n f = x ↓ ↓ Wrong
n f – n P = x ↓ ↓ Correct
⇒ ⇒ n P = n f – x = 256 – 5 Hz.
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