Question

In sound frequency analysis, the lower and upper frequencies of a 1/1 octave band are 710 Hz and 1420 Hz respectively. The centre frequency of the band in Hz is \(\underline{\hspace{1cm}}\). (round off to the nearest integer)

Hint:

The centre frequency of an octave band is always the geometric mean of the band limits.

Answer 1

Correct Answer: 999

For an octave band, centre frequency is the geometric mean of the lower and upper frequencies:
\[ f_c = \sqrt{f_1 f_2} \] \[ f_c = \sqrt{710 \times 1420} = \sqrt{1008200} \] \[ f_c \approx 1004.09 \] Rounded to nearest integer:
\[ \boxed{1004\ \text{Hz}} \]