While demonstrating beats to a class, a teacher notices that the audible waxing and waning suddenly vanish when the difference between the fork frequencies is increased beyond a certain value.
(i) Explain qualitatively why two sound waves of widely different frequencies do not produce perceivable beats even though the principle of superposition still holds.
(ii) A tuning fork of frequency 512Hz is slightly filed so that its frequency increases. Predict and explain the qualitative change in the beat frequency heard when it is struck together with another fork of fixed frequency 500Hz.
(iii) Describe how you would use the phenomenon of beats to determine whether a laboratory tuning fork labelled 256Hz is actually above or below this value.