A tube closed at one end has a vibrating diaphragm at the other end, which may be assumed to be displacement node. It is found that when the frequency of the diaphragm is 2000 Hz, then a stationary wave pattern is set up in which the distance between adjacent nodes is 8 cm. When the frequency is gradually reduced, then the stationary wave pattern disappears but another stationary wave pattern reappears at a frequency of 1600 Hz. Calculate
(i) The speed of sound in air,
(ii) The distance between adjacent nodes at a frequency of 1600 Hz,
(iii) The distance between the diaphragm and the closed end, and
(iv) The next lower frequencies at which stationary wave pattern will be obtained.