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Question
A steel wire fixed at both ends has a fundamental frequency of 200 Hz. A person can hear sound of maximum frequency 14 kHz. What is the highest harmonic that can be played on this string which is audible to the person?
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Solution
Given:
Fundamental frequency (f0) of the steel wire = 200 Hz
Let the highest harmonic audible to the person be n.
Frequency of the highest harmonic, f' = 14000 Hz
∴ f'=nf0 ...(1)
\[\frac{f'}{f_0} = \frac{14000}{200}\]
\[ \Rightarrow \frac{n f_0}{f_0} = 70\]
\[ \Rightarrow n = 70\]
Thus, the highest harmonic audible to man is the 70th harmonic.
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