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 70^th harmonic.

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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?

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) f'f0=14000200⇒nf0f0=70⇒ n=70 Thus, the highest harmonic audible to man is the 70th harmonic.