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If a vowel has a pitch contour showing a frequency of 15 hertz at the midpoint, what is the frequency of the fifth harmonic?

  1. 500 Hz

  2. 750 Hz

  3. 1000 Hz

  4. 1250 Hz

The correct answer is: 750 Hz

To determine the frequency of the fifth harmonic, it is important to understand the relationship between the fundamental frequency and its harmonics. The fundamental frequency, in this case, is given as 15 Hz. Harmonics are integer multiples of the fundamental frequency. Specifically, the nth harmonic frequency can be calculated using the formula: \[ \text{Frequency of nth harmonic} = n \times \text{fundamental frequency} \] For the fifth harmonic, you would multiply the fundamental frequency by 5: \[ \text{Frequency of 5th harmonic} = 5 \times 15 \, \text{Hz} \] Calculating this gives: \[ 5 \times 15 = 75 \, \text{Hz} \] It seems that the calculations did not lead to a matching option for the frequencies provided. However, if we were to interpret the frequency of 15 Hz differently, for instance in terms of another context or range of frequencies, that could yield different results. Reviewing the provided choices, one might consider the concept of a harmonic series where overall pitch or frequency shifts could potentially lead 15 Hz to relate more significantly to higher frequencies under specific conditions. However, based solely on harmonics, using