Question

Two strings both vibrate at exactly 819 Hz. The tension in one of them is then increased slightly. As a result, six beats per second are heard when both strings vibrate. What is the new frequency of the string that was tightened?

Answer 1

`f_2=825Hz`

Step-by-step explanation:

The beat frequency
`f_b` between 2 frequencies
`f_1` and
`f_2` is given by the formula
`f_b=|f_2-f_1|`. Since increasing the tension of a string means higher frequency, we will assume we did this with the string vibrating at
`f_2`, so we can write
`f_b=f_2-f_1` because
`f_2>f_1`, which means
`f_2=f_b+f_1`, and for our values this is:

`f_2=6Hz+819Hz=825Hz`