Question

A musical instrument produces a frequency of 450 Hz when it vibrates in the fifth harmonic. The fundamental frequency of this instrument is ________ Hz.

Answer 1

The frequency of the nth harmonic is related to the fundamental harmonic by the equation:

$f_n=nf_1$

In this case we know the fifth harmonic, that is n=5 and f5=450, then we have:

$\begin{gathered} 450=5f_1 \\ f_1=\frac{450}{5} \\ f_1=90 \end{gathered}$

Therefore, the fundamental harmonic is 90 Hz