Normal modes of strings and pipes

You will list the natural frequencies of a string and of two kinds of pipe, and count the notes below a limit.

The idea.

• A string tied at both ends: $f_n = \dfrac{n}{2L}\sqrt{\dfrac{T}{\mu}}$ for $n = 1, 2, 3, \ldots$
• A pipe open at both ends: $f_n = \dfrac{nv}{2L}$.
• A pipe closed at one end: $f = \dfrac{(2n - 1)v}{4L}$, odd harmonics only.

Your tasks.

1. In string_modes, return the first count frequencies of the string.
2. In open_pipe, return the first count frequencies of an open pipe.
3. In closed_pipe, return the first count frequencies of a closed pipe.
4. In below, return how many frequencies in a list are less than limit.