Question

A person is tuning a piano, using $512Hz$ tuning fork, trying to match this frequency to the frequency of the note produced by the piano. The person hears a pitch close to $512Hz$ that gets loud and soft four times each second.
What is a possible value of the current frequency of the note produced by the piano?

• A. $508Hz$
• B. $128Hz$
• C. $2048Hz$
• D. $512Hz$
• E. None of the listed frequencies are possible

Answer 1

The correct option is A $508Hz$

Beat frequency $b=4$ $Hz$ (given)

Original frequency of the sound ${\nu }_1=512$ $Hz$

Using $b=|{\nu }_1-{\nu }_2|$

$\therefore$ $4=|512-{\nu }_2|$ $⟹{\nu }_2=508$ $Hz$ OR $516$ $Hz$