Question

A guitarist tunes one of her strings to a 440 Hz tuning fork. Initially, a beat frequency of 5 Hz is heard when the string and tuning fork are sounded. When the guitarist tightens the string slowly and steadily, the beat frequency decreases to 4 Hz. What was the initial frequency of the string?

Answer 1

Frequency of tuning fork is

When string and tuning fork are sounded, beat frequency heard is

Beat frequency is the difference in frequencies of tuning fork and string, so the frequency of string must be either or

When the guitarist tightens the string, beat frequency

So after the string is tightened , frequency of string must be either or

the tension of string is more when compared to initial tension of the string because the string is tightened.

  

Using

ratio of frequencies of string initially and finally is ( since )

Which is possible when and

So the initial frequency of the string is