Answer 3

If a 220-Hz sinusoid sampled at $f_{s1} = 44100$ Hz is played back at $f_{s2} = 22050$ Hz ($f_{s1}/2$), then the

• period between the samples will be twice as long:
  $$T_{s2} = \frac{1}{f_{s2}} = \frac{1}{22050} = \frac{2}{44100} = \frac{2}{f_{s1}},$$

• and the period of oscillation will double:
  $$T_2 = 2T_1 = \frac{2}{f_1} = \frac{2}{220}$$    s$$,$$

• and the corresponding frequency will be halved (sound an octave lower):
  $$f_2 = \frac{1}{T_2} = \frac{220}{2} = 110$$    Hz$$.$$