When a tuning fork is excited, molecules of air vibrate in accordance with the equation x = A cos(512πt). When this tuning fork and another identical tuning fork loaded with a little wax are excited together, 4 beats are heard. What is the frequency of the second fork loaded with wax.

When the first tuning fork is excited, the vibrations of the air molecules are simple harmonic with angular frequency ω = 512π as is evident from the form of the equation, x = A cos(512πt). The linear frequency of vibration of the first fork is n = ω/2π = 512π/2π = 256 Hz. The frequency of the 2nd tuning fork before loading with wax was therefore 256 Hz. After loading with wax, its frequency is lowered. 

Since the beat frequency is 4 Hz, its frequency (after loading) is 256 – 4 = 252 Hz.