Question

One of the harmonic frequencies for a particular string under tension is 325Hz. The next higher harmonic frequency is 390Hz.
What harmonic frequency is next higher after the harmonic frequency \[195Hz\]?

Answer 1

Hint: The harmonics are positive integer multiples of the fundamental frequency. Here, two successive harmonic frequencies are given. The difference between two successive pairs of the harmonic frequencies is equal to the fundamental frequency. Using this relation, we can solve the above question.

Formula used:
\[{{f}_{fundamental}}={{f}_{2}}-{{f}_{1}}\]

Complete step by step solution:
 Given,
 Two successive harmonic frequencies of a string under tension are \[325Hz\] and \[390Hz\].
 \[{{f}_{1}}=325Hz\]
\[{{f}_{2}}=390Hz\]
 The difference between two successive pairs of the harmonic frequencies is equal to the fundamental frequency.
 Then,
 \[{{f}_{fundamental}}={{f}_{2}}-{{f}_{1}}\]
 Substituting the values of \[{{f}_{1}}\text{ and }{{f}_{2}}\], we get,
 \[{{f}_{fundamental}}=390-325=65Hz\]
Then,
 The next higher harmonic frequency after the harmonic frequency \[195Hz\]\[=195+65=260Hz\]

Additional information:
Natural frequencies that an instrument or object produces have its own standing wave pattern or characteristic vibrational mode. These patterns are only created within the instrument or object at a specific frequency of vibration; this frequency is called the harmonic frequency or harmonics. At any frequency other than a harmonic frequency, the resulting disturbance of the medium is non-repeating and irregular. The harmonics frequencies are positive integer multiples of the fundamental frequency

Note:
Harmonics are usually produced as a result of oscillations. Partial harmonics will produce different frequencies than that of full Harmonics. Long and thin wired instruments can produce exact harmonic frequencies. The harmonic spectrum of the sound is made up by higher frequency harmonics that sound above the fundamental frequency.