Answer 2 (Method 2)

If $f_s = 16$, what is the frequency of the sinusoid?

Method 2: the period of the sinusoid is

$$T = 8 \times T_s = \frac{8}{16} = \frac{1}{2},$$

and the frequency is

$$f = \frac{1}{T} = \frac{1}{2} = 2$$    Hz$$.$$

If $f_s = 32$, then the frequency is higher:

$$f = \frac{1}{T} = \frac{32}{8} = 4$$    Hz$$.$$