Question

If a wave's third harmonic has a frequency of 24 Hz, what is its

Answer 1

Answer:

8 Hz, 48 Hz

Explanation:

The standing waves on a string (or inside a pipe, for instance) have different modes of vibrations, depending on how many segments of the string are vibrating.

The fundamental frequency of a standing wave is the frequency of the fundamental mode of vibration; then, the higher modes of vibration are called harmonics. The frequency of the n-th harmonic is given by

$f_n = nf_1$

where

$f_1$ is the fundamental frequency

In this problem, we know that the wave's third harmonic has a frequency of

$f_3=24 Hz$

This means this is the frequency for n = 3. Therefore, we can find the fundamental frequency as:

$f_1=\frac{f_3}{3}=\frac{24}{3}=8 Hz$

Now we can also find the frequency of the 6-th harmonic using n = 6:

$f_6 = 6 f_1 = 6 (8)=48 Hz$