Question

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

Answer 1

258 Hz or 266 Hz

Step-by-step 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:

`f_B = |f_1 -f_2|`

where

`f_B` is the beat frequency

`f_1` is the frequency of the 1st sound

`f_2` is the frequency of the 2nd sound

In this problem,

`f_B=4 Hz` is the beat frequency

`f_1=262 Hz` is the frequency of the middle C tuning fork

`f_2` is the frequency of the middle C piano string

Solving for f2, we find two solutions:

`f_2=f_1-f_B = 262-4 = 258 Hz\\f_2 = f_1+f_B = 262+4=266 Hz`