Answer
See explanation.
Work Step by Step
The speed of a wave on a string, as shown in equation 15.14, depends on the tension and linear mass density.
$$v=\sqrt{\frac{F}{\mu}}$$
The waves travel faster on the thin string, which has a lower mass per meter
$\mu$.
The fundamental frequency is proportional to the wave speed v, as shown by equation 15.33, so the thin strings will have a higher fundamental vibration frequency.
