Question

A 487-Hz tuning fork is sounded together with an out-of-tune guitar string, and a beat frequency of 4 Hz is heard. When the string is tightened, the frequency at which it vibrates increases, and the beat frequency is heard to decrease. What was the original frequency of the guitar string?

Answer 1

Answer:

$f_{frequency}=483Hz$

Explanation:

Let f is frequency of of the guitar string

Frequency of tuning fork is given 487 Hz

Beat frequency is difference frequencies of guitar string and the tuning fork

It could be

(f - 487Hz)

or

(487Hz-f)

As it is mentioned that as the frequency of guitar string increases the beat frequency decreases

So the beat frequency is given as

$f_{frequency}=(487Hz-f)\\f_{frequency}=(487-4)\\ f_{frequency}=483Hz$