Question

The following figure depicts a spectrum of a vowel (dashed line), where $F_0 = 150$ Hz and $F_0 = H1$. The harmonics are indicated from $H1$ to $H11$. From the figure, the frequency (in Hz) of the second formant ($F2$) of this vowel is __________

Hint:

Formant peaks are read off the envelope, not the harmonic lines. Once you identify the nearest $Hn$, multiply $n$ by $F_0$ to get the frequency.

Answer 1

Step 1: Map harmonics to frequencies.
Given $F_0=150$ Hz and $F_0=H1$, the $n^\text{th}$ harmonic is $Hn=n\times 150$ Hz.
Thus: $H1=150$, $H2=300$, $H3=450$, $\dots$, $H9=9\times150=1350$ Hz, etc.

Step 2: Locate $F2$ on the spectral envelope.
From the dashed spectral envelope, the second formant peak aligns near the vertical line at $H9$.

Step 3: Read the frequency.
$F2 \approx$ frequency at $H9 = 1350$ Hz.
\[ \boxed{F2 = 1350\ \text{Hz}} \]