If a wave's third harmonic has a frequency of 24 Hz, what is its
natural (fundamental) frequency and what is the frequency of H6?

Respuesta :

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

[tex]f_n = nf_1[/tex]

where

[tex]f_1[/tex] is the fundamental frequency

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

[tex]f_3=24 Hz[/tex]

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

[tex]f_1=\frac{f_3}{3}=\frac{24}{3}=8 Hz[/tex]

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

[tex]f_6 = 6 f_1 = 6 (8)=48 Hz[/tex]