Answer: 58.8Hz
Explanation:
Harmonics or overtones are multiple integrals of the fundamental frequencies. Sound waves can occur both in closed pipes, open pipes and strings.
First we need to get the fundamental frequency in open pipes.
Note that frequency = velocity/wavelength
The length of the pipe (L) with fundamental frequency in term of its wavelength is ¶/2 (taking ¶ as wavelength)
L = ¶/2
¶ = 2L
Substituting this in the fundamental frequency formula
Fo = v/¶
Fo = v/2L
Since v = 333m/s
L = 8.5m
Fo = 333/2(8.5)
Fo = 333/17
Fo = 19.6Hz
This fundamental frequency will be the first harmonics
First overtone (f1) will be the second harmonics f1 = 2fo
Second overtone (f2) will then be third harmonics f2 = 3fo
f2 = 3×19.6
F2 = 58.8Hz
Third harmonic frequency will be 58.8Hz
*Check attachment for diagram
The third frequency of the standing waves traveling in a pipe of length 8.5m is 58.7647 Hz.
Given to us
Length of the pipe, L = 8.5 m
speed of the sound in the column, v = 333 m/s
The wavelength of the sound can be given as,
Wavelength, λ = 2L
λ = 2 x 8.5
λ = 17 meters
The harmonic frequency can be given as,
[tex]f = \dfrac{v}{\lambda}[/tex]
substitute the values,
[tex]f = \dfrac{333\rm\ m/s}{17\rm\ meters}[/tex]
[tex]f= 19.5882\rm\ Hz[/tex]
We got the frequency of the wave, now calculating the third harmonic frequency,
[tex]f_3 = 3f[/tex]
[tex]\begin{aligned}f_3&=3\times 19.5882\\\\&= 58.7647\ Hz\end{aligned}[/tex]
Hence, the third harmonic frequency of the standing waves traveling in a pipe of length 8.5m is 58.7647 Hz.
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