If the length of a vibrating string is changed from l1 to l2=l1/3 while keeping tension and linear density constant, what is the new frequency f2 in terms of the original frequency f1?

Step 1: The fundamental frequency is given by
$f = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$

Step 2: Assuming $T$ and $\mu$ are constant,
$f \propto \frac{1}{l}$

Step 3: Therefore, for two cases,
$f_1 l_1 = f_2 l_2$

Step 4: Given $l_2 = \frac{l_1}{3}$, substitute:
$f_1 l_1 = f_2 \left( \frac{l_1}{3} \right)$

Step 5: Solve for $f_2$:
$f_2 = f_1 l_1 \div \frac{l_1}{3}$
$f_2 = f_1 l_1 \times \frac{3}{l_1}$
$f_2 = 3 f_1$

$\boxed{f_2 = 3f_1}$