Answer:
Explanation:
In audio and frequency analysis, a decade represents a tenfold increase in frequency. An octave, on the other hand, represents a doubling of frequency.(a) To calculate the number of 1/3 octaves in a decade, we need to consider how many times we can divide a decade into 1/3 octave intervals.A decade represents a tenfold increase in frequency. To find the number of 1/3 octaves, we can calculate:Number of 1/3 octaves in a decade = 10 (decades) / (1/3)Now, divide 10 by 1/3:Number of 1/3 octaves = 10 / (1/3) = 10 * (3/1) = 30So, there are 30 1/3 octaves in a decade.(b) To calculate how many octaves are in a decade, we need to determine how many times a frequency doubles in a decade.As mentioned earlier, a decade represents a tenfold increase in frequency. In each octave, the frequency doubles. So, to find the number of octaves in a decade, we can calculate:Number of octaves in a decade = Log2(10)Using logarithm base 2, we can find:Number of octaves = Log2(10) ≈ 3.32193 (rounded to 5 decimal places)So, there are approximately 3.32193 octaves in a decade. If you want the answer in whole numbers, you can round it to 3 octaves.