Question

Tuning a guitar string, you play a pure 330 Hz note using a tuning device, and pluck the string. The combined notes produce a beat frequency of 5 Hz. You then play a pure 350 Hz note and pluck the string, finding a beat frequency of 25 Hz. What is the frequency of the string note?

Answer 1

Answer:

The  frequency is  $F = 325 Hz$

Explanation:

From the question we are told that

    The frequency for the first note is  $F_1 = 330 Hz$

     The  beat frequency of the first note is  $f_b = 5 \ Hz$

     The  frequency for the second note is  $F_2 = 350 \ H_z$

      The  beat frequency of the first note is $f_a = 25 \ Hz$

Generally beat frequency is mathematically represented as

        $F_{beat} = | F_a - F_b |$

Where $F_a \ and \ F_b$ are frequencies of two sound source

  Now in the case of this question

For the first note

     $f_b = F_1 - F \ \ \ \ \ ...(1)$

Where  F is the frequency of the string note

For the second note  

      $f_a = F_2 - F \ \ \ \ \ ...(2)$

Adding  equation 1 from 2

      $f_b + f_a = F_1 + F_2 + ( - F) + (-F) )$

      $f_b + f_a = F_1 + F_2 -2F$

substituting values

       $5 +25 = 330 + 350 -2F$

=>     $F = 325 Hz$