Organ pipe "Y" (open at both ends) is half as long as organ pipe "X" (open at One end as shown. The ratio of their fundamental frequencies fx:fv is:

Explanation

An organ pipe open at both ends (Pipe Y) has a fundamental frequency given by f = v/(2L), where v is the speed of sound and L is the length of the pipe. An organ pipe open at one end and closed at the other (Pipe X) has a fundamental frequency given by f = v/(4L). Since Pipe Y is half the length of Pipe X, its fundamental frequency is twice the fundamental frequency of an open-open pipe of the same length. Thus, the fundamental frequency of Pipe Y is four times that of Pipe X. Therefore, the ratio of their fundamental frequencies fx:fy is 1:4. The other options do not account for the differences in pipe lengths and end conditions appropriately, hence they are incorrect.