Question

Chelsea is tuning a piano when She discovers that G above middle C is vibrating with a higher frequency than her G tuning fork, which vibrates at 392 Hz. She plays the piano key and tuning fork at the same time and hears a beat frequency of 2.0 Hz. What is the frequency of the G on the piano.

Answer 1

F = 392 + 2 = 394 Hz

Answer 2

Piano strings have Inharmonicity. It means you need to tune the notes a bit sharper than a tuning fork as you go higher than the middle octave. If you don`t do that , when you play the octave on a piano , it will sound horrible .The opposite effect happens below the middle octave.You need to tune them progressively lower compared to tuning forks.
Also , each piano has it`s own personal amounts of inharmonicity. Smaller pianos have more inharmonicity than large Grand Pianos . It`s all caused by the stiffness of the strings .(Mainly the end bits).