Final answer:
The flute's range from C4 to D7 covers a little more than 3 octaves, as D7 is beyond C7 but does not reach 4 full octaves. The correct answer is option (a) 3.
Step-by-step explanation:
The question asks how many octaves the range of a flute encompasses, from C4 (261.63 Hz) to D7 (2349.32 Hz). An octave is a doubling or halving of a frequency. To determine the number of octaves, we find the number of times the frequency can be doubled starting from C4 until it exceeds or equals D7.
Starting with 261.63 Hz (C4):
- Double 261.63 Hz to reach 523.26 Hz (C5)
- Double 523.26 Hz to reach 1046.52 Hz (C6)
- Double 1046.52 Hz to reach 2093.04 Hz (C7)
Since D7 (2349.32 Hz) is higher than C7 but not double, the range covers a little more than 3 octaves but not quite 4 octaves. Therefore, the correct answer is 3 octaves, represented as option (a) 3.