In an organ pipe whose one end is at x =0, the pressureis expressed by `P = P_(0) "cos" (3 pi x)/(2) sin 300 pi t` where x is in meter and t in sec. The organ pipe can be :-

Options

A. Closed at one end, open at another with length = 0.5 m
B. Open at both ends, length = 1m
C. Closed at both ends, length = 2 m
D. Closed at one end, open at another with length = 2/3 m

Answer

D

Explanation

`(3pi)/(2)=(2pi)/(lamda)rArr lamda=(4)/(3)m`
Pr. Amp. `=P_(0)cos((3pix)/(2))=P_(0)` at `x=0`
`P_(0)cos ((3pix)/(2))=P_(0)`
and `-P_(0)`at `x=2//3=P_(0)` at `x=4//3`
`:.` Pipe may be closed at x =0 and open at `x = (2)/(3)m`
`x = (2)/(3)m`