Should the D String Be Tightened or Loosened When Tuning a Banjo?

[nczzzzzz]

Homework Statement

One way to tune a banjo to itself is to fix the frequency of one string (say, the "A" string) and compare the frequency of the "D" string while held at the seventh fret (so that it should also produce an "A"). If the "D" string is tuned correctly, then the "A" played by the pinched "D" string and the open "A" string should be the same frequency.

Suppose the two "A" notes produce a tone with a beat frequency of 5 Hz. Should the "D" string be tightened or loosened?

A. It should be tightened.

B. It should be loosened.

Homework Equations

v=f*λ

The Attempt at a Solution

 

[CWatters]

What was option C. ?