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.