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Many opera singers have a range of about 2.5 octaves or even greater. What is the approximate frequency range for a singer with a 2.5-octave range?

a) 120 Hz to 480 Hz
b) 240 Hz to 960 Hz
c) 480 Hz to 1920 Hz
d) 960 Hz to 3840 Hz

1 Answer

4 votes

Final answer:

To find the frequency range for a singer with a 2.5-octave range, we take the lower boundary of their range and multiply it by 2 to the power of 2.5. The provided options do not directly match the calculation, suggesting an error or the need for additional context regarding the singer's range starting point.

Step-by-step explanation:

An opera singer with a 2.5-octave range would have a frequency range that depends on their starting frequency.

An octave represents a doubling or halving of a frequency. So, to calculate the frequency range, we would take the starting frequency and multiply it by 2 to the power of 2.5 (since an octave is a doubling of frequency).

Let's assume the lowest frequency the singer can reach is 120 Hz. Therefore, to find the high end of their range we calculate:

120 Hz × 22.5 = 120 Hz × 5.66 ≈ 680 Hz.

This range isn't listed among the provided options, which suggests the need for considering different starting frequencies. If we consider a starting frequency of 240 Hz, then:

240 Hz × 22.5 = 240 Hz × 5.66 ≈ 1360 Hz.

Among the given options, option b, which is 240 Hz to 960 Hz, is the closest to our calculation. However, a precise range should ideally align with one of the specific options provided, indicating the need for further clarification.

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