The frequency of the 10th harmonic is 800 Hz
Explanation:
The frequency of the nth-harmonic for the standing waves in a string is given by the equation
[tex]f_n = n f_1[/tex]
where
[tex]f_1[/tex] is the fundamental frequency of the string
In this problem, we are given the frequency of the 3rd harmonic:
[tex]f_3 = 240 Hz[/tex]
Which can be rewritten in terms of the fundamental frequency
[tex]f_3 = 3 f_1[/tex]
So we find [tex]f_1[/tex]:
[tex]f_1 = \frac{f_3}{3}=\frac{240}{3}=80 Hz[/tex]
Now that we have the fundamental frequency, we can find the frequency of the 10th harmonic, with n = 10 :
[tex]f_{10} = 10f_1 = (10)(80)=800 Hz[/tex]
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