Answer
Listen for beats between the tuning fork and the piano string's second harmonic.
Work Step by Step
When a properly tuned A3 piano string is played/plucked, it will oscillate at 220 Hz, but the waveform will also contain partial tones at its second harmonic.
As seen on page 395 and in Figure 21.5, the second harmonic is at two times the fundamental frequency, or $2 f_{o}$.
If the string is not properly tuned, its second harmonic will not be at 440 Hz, and will beat against the 440 Hz tone generated by the tuning fork. Tighten or loosen the piano string until the beats cannot be heard.
