## Related questions with answers

Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. If one is vibrating at 132 Hz, what must be the frequency of the other (is there only one answer)?

Solutions

Verified### Finding $f_2$

One string vibrates at $f_1=132\text{Hz}$. When played at the same time with the other string, the frequency of beats heard is $\Delta f=\dfrac{2}{3\text{s}}=1.5\text{Hz}$. We want to find the possible values of the frequency of the unknown string, $f_2$.

The frequency of the unknown string is equal to

$\begin{align*} f_2&=f_1\pm \Delta f \\ &=132\text{Hz}\pm 1.5\text{Hz} \\\\ \boxed{f_2=133.5\text{Hz}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&\text{or} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \boxed{f_2=130.5\text{Hz}} \,. \end{align*}$

Beat frequency is 1.5Hz. (3/2)Hz.

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