A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is

Question

Philoid · Accepted Answer

The frequency of beats ν = |ν₁-ν₂| = 6 Hz where ν₁ = 512 Hz, ν₂ = frequency of sonometer. Thus ν₂ is either 506 or 518 Hz.
When the tension in the string is slightly increased the frequency of the sonometer slightly increases. Since the beat frequency reduces it means ν₂<ν₁ so ν₂ is 506 Hz.

Option A is correct.