The physics
A sonometer wire rests on two bridges. The gap between them, l, is the part that rings. A hanging load gives the tension, T = Mg.
In its lowest note, the wire holds one loop. One loop is half a wave, so λ = 2l.
f = (1/2l) √(T/μ)
Strike a tuning fork on the box. The wire rings only when its own note matches the fork. Then a paper rider at the middle of the gap jumps off.
The laws: with the wire and load the same, f × l stays fixed. With the gap the same, f grows as √T. A thicker wire has more mass per metre: μ = πr²ρ.
f₁ l₁ = f₂ l₂ f ∝ √T f ∝ 1/r
Pitch goes up with frequency. One octave up doubles it. A load hanging in water pulls less: T = (m − ρV)g.