An air column of length L is open at one end and closed at the other. A narrow sound pulse of angular frequency ω and amplitude P0 is sent down the column from the open end toward the closed end.
(a) Treat the closed end as a rigid boundary and write the pressure equation for the reflected pulse.
(b) Superpose the incident and reflected disturbances to obtain the expression for the stationary pressure variation p(x,t) inside the column.
(c) Show that a displacement antinode coincides with the open end while a displacement node coincides with the closed end.
(d) Hence, derive the condition for the fundamental mode of vibration of the air column and state its wavelength in terms of L.