Our local piano tuner is making a house call to tune our piano (... yes, she's maintaining social distance!) She strikes a middle C tuning fork (about 262 Hz frequency), and strikes that key on your piano. You both hear a beat frequency of about 4 Hz. What is the actual frequency of your middle C piano string

258 Hz or 266 Hz

Explanation:

When two sounds of similar frequency occur at the same time, a phenomenon called "beat" occurs. The beat is an interference patter between the two sounds; the frequency of this beats (called beat frequency) is given by the difference between the frequencies of the two sounds:

where

is the beat frequency

is the frequency of the 1st sound

is the frequency of the 2nd sound

In this problem,

is the beat frequency

is the frequency of the middle C tuning fork

is the frequency of the middle C piano string

Solving for f2, we find two solutions:

no simpler subs form complex ones. synthesise = make

more than, less

less than, more