Answer:
λ = V / f the wavelength versus the frequency
V = f λ and V (speed) proportional λ for a fixed frequency
F = f^2 * (M / L) * λ^2 = (f * λ)^2 * (M / L)^2 force (tension) on string at a given frequency
F2 / F1 = (λ2 / λ1)^2 other items are constant
Let λ1 = 6 then λ2 must be 3/2 λ1 for a constant length
F2 / F1 = (6 / 4)^2 = 9/4
The tension must be increased to 9 / 4 of the original tension
Check: if the frequency is fixed then V will be larger for a larger wavelength (situation 2)
One can also write V = (F / (M / L))^1/2
Then for fixed M L
F2 / F1 = (V2 / V1)^2
Since V = f λ Velocity is proportional to λ for a fixed frequency
Then if V2 / V1 = 3 / 2 F2 = 9/4 F1
