Question

A piano tuner hears a beat every 2.20 s when listening to a 266.0 Hz tuning fork and a single piano string. What are the two possible frequencies (in Hz) of the string? (Give your answers to at least one decimal place.)

Answer 1

Answer:

The lower frequency is $f_1 = 265.55 \ Hz$

The higher frequency is  $f_2 = 266.4546 \ Hz$

Explanation:

From the question we are told that

     The period is   $T = 2.20 \ s$

      The frequency of the tuning fork is  $f = 266.0 \ Hz$

Generally the beat frequency is mathematically represented as

       $f_b = \frac{1}{T}$

substituting values

      $f_b = \frac{1}{2.20}$

      $f_b = 0.4546 \ Hz$

Since the beat  frequency is gotten from the beat produced by the tuning fork and and  the string   then

The possible frequency of the string ranges from

     $f_1 = f- f _b$

to

    $f_2 = f + f_b$

Now  substituting values

    $f_1 = 266.0 - 0.4546$

    $f_1 = 265.55 \ Hz$

For  $f_2$

    $f_2 = 266 + 0.4546$

    $f_2 = 266.4546 \ Hz$