Is the sinusoidal pattern on a string longer or shorter when there is a greater propagation velocity?

We know that

Velocity= wavelength x frequency

And f= 1/2π√T/u

So we also know that

The frequency of nth harmonic standing wave is

fn=nv/2L

So from the relationships above

We can see that as propagational velocity increases, the frequency increases and the wavelength decreases. So finally we can say that sinusoidal pattern on a string is shorter when there is a greater propagation velocity

where is the photo and the answer choices?