In: Physics
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?
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