Two tuning forks F1 and F2, having frequencies 256Hz and 260Hz respectively, are sounded together near an ear. Each fork produces the same displacement amplitude a at the ear.
(i) Assuming both waves travel in the same direction, write the expression for the instantaneous resultant displacement heard at the ear.
(ii) Show, by suitable algebraic steps, that the loudness heard varies periodically in time and obtain an expression for the beat frequency.
(iii) How much time elapses between successive maxima of loudness?
(iv) One of the forks is now loaded uniformly with wax so that the beat frequency falls to 2 Hz. Determine the new frequency of the loaded fork.