Give the equation for the normal modes of vibration for a closed pipe.

(N/A) For a pipe closed at one end and open at the other,the boundary conditions require a node at the closed end and an antinode at the open end.
Let $L$ be the length of the pipe and $v$ be the speed of sound in air.
The wavelength $\lambda_n$ of the $n$-th harmonic is given by $\lambda_n = \frac{4L}{n}$,where $n = 1, 3, 5, \dots$ (only odd harmonics).
The frequency $f_n$ of the $n$-th normal mode is given by $f_n = \frac{v}{\lambda_n} = \frac{nv}{4L}$ for $n = 1, 3, 5, \dots$.