Explain why a pipe closed at one end gives only the odd harmonics, while a pipe open at both ends…

Step 1. (a) A closed pipe has a node at one end and an antinode at the other. So it holds an odd number of quarter wavelengths, $L = (2n - 1)\dfrac{\lambda}{4}$, which gives only $f_1$, $3f_1$, $5f_1$ and so on. An open pipe has antinodes at both ends and holds any whole number of half wavelengths.

Step 2. (b) $f_1 = \dfrac{340\ \text{m/s}}{4 \times 0.5\ \text{m}} = 170\ \text{Hz}$, then $3 \times 170\ \text{Hz} = 510\ \text{Hz}$.