A pipe closed at one end has a physical length of 60 cm and contains air at 25 °C where the speed of sound is 346 m s⁻¹.
(i) Show that a note of frequency 660 Hz cannot correspond to the fundamental mode of this pipe.
(ii) Find the mode number (n = 1, 2, 3, …) for which the pipe will resonate closest to 660 Hz and calculate that resonant frequency.
(iii) Compute the frequency gap between this resonance and the next higher resonance of the pipe.