Question

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?

Answer 1

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

Step-by-step 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 .