Beat frequencies can be used to measure the pitch of an unknown sound even if it normally would be outside the audible range. For example, a certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.
(kHz)