Answer
(a) The length of the pipe should be $0.328~m$
(b) The fundamental frequency is $252.3~Hz$
Work Step by Step
(a) We can find the length of the pipe:
$\lambda = \frac{v}{f}$
$4L = \frac{v}{f}$
$L = \frac{v}{4f}$
$L = \frac{343~m/s}{(4)(261.5~Hz)}$
$L = 0.328~m$
The length of the pipe should be $0.328~m$
(b) At a temperature of $0.0^{\circ}C$, the speed of sound in air is $331~m/s$. We can find the fundamental frequency:
$f = \frac{v}{\lambda}$
$f = \frac{v}{4L}$
$f = \frac{331~m/s}{(4)(0.328~m)}$
$f = 252.3~Hz$
The fundamental frequency is $252.3~Hz$
