#### Answer

The closest distance between nodes is:
(c) $~\frac{2}{7} L$

#### Work Step by Step

For a pipe that is closed at one end, the wavelength is $\lambda_n = \frac{4L}{n}$
If the frequency of the standing wave is seven times the fundamental frequency, then $n=7$ and $\lambda_7 = \frac{4L}{7}$
Since there is a node at each half-cycle, the distance between each successive node is $\frac{\lambda_7}{2} = \frac{2L}{7}$
The closest distance between nodes is:
(c) $~\frac{2}{7} L$