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 = (f_4)/(4)= (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.