Suppose you sound a 1056-hertz tuning fork at the same time you strike a note on the piano and hear 2 beats/second. You tighten the piano string very slightly and now hear 3 beats/second. What is the frequency of the piano string?

The frequency of the piano string is either 1053 HZ or 1059 HZ.

Explanation:

Here we know that frequency of beats is equal to the difference between the frequencies between two waves .

     Given that frequency of tuning fork is 1056 HZ  .

     Let the frequency of the piano be ' f ' .

   Given that number of beats = 3.

    We know that   | 1056 - f | = 3 ;

                      ⇒       1056- f = ±3,

         Upon solving this we get  

                        f = 1056-3 and 1056 + 3

                   ⇒ f = 1053 or 1059 .

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