Q.A standing wave is produced in a tube open at both ends. The fundamental frequency is 300 Hz. What is the length of tube in the fundamental mode? (speed of the sound= 340 m s-1).

A pipe open at BOTH ends must have an ANTINODE at each open end (both ends being comparatively free, each formed slightly beyond its own physical opening per the end correction). The fundamental mode fits exactly half a wavelength into the corrected air-column length L (an antinode at each end, one node in between), so $L=\lambda/2$, giving fundamental frequency $n=v/2L$. Because BOTH boundary conditions are of the SAME kind (antinode at each end, unlike the closed-pipe case), each successive allowed mode can add just ONE more half-wavelength segment at a time, so the general p-th overtone has frequency $n_p=(p+1)n$. …