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

Answer:

$f_2=825Hz$

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:

$f_2=6Hz+819Hz=825Hz$