Question

A string fixed at both ends has a length of 1m. With the frequency 0f 44kHz (fourth overtone) standing waves are produced . which harmonics will be audible to humans?

Answer 1

The frequency of the nth-harmonic is an integer multiple of the fundamental frequency of the string:
$f_n = n f_1$
where $f_1$ is the fundamental frequency.

Here, we know the frequency of the 4th harmonic $f_4 = 44 kHz$, therefore we can use it to find the fundamental frequency and the following overtones:
$f_1 = \frac{f_4}{4}= \frac{44 kHz}{4}=11 kHz$
$f_2 = 2 f_1 = 2 \cdot 11 kHz =22 kHz$
$f_3 = 3 f_1 = 3 \cdot 11 kHz = 33 kHz$

Since the hearing range of human ear goes from 20 Hz to 20 kHz, it means that only the first harmonic of 11 kHz will be audible to humans.