Final answer:
The first three overtones of an alto clarinet with a fundamental frequency of 90 Hz, acting as a tube closed at one end, are 270 Hz, 450 Hz, and 630 Hz, representing the 3rd, 5th, and 7th harmonics respectively.
Step-by-step explanation:
When dealing with the overtones of a musical instrument such as an alto clarinet, which behaves like a tube closed at one end and open at the other, it’s important to understand the harmonic series for such an instrument. For a tube closed at one end, the harmonic frequencies are the odd multiples of the fundamental frequency. Given that the fundamental frequency of the alto clarinet is 90.0 Hz, we can calculate the first three overtones.
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- First overtone (3rd harmonic): 3 × 90.0 Hz = 270 Hz
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- Second overtone (5th harmonic): 5 × 90.0 Hz = 450 Hz
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- Third overtone (7th harmonic): 7 × 90.0 Hz = 630 Hz
Thus, the alto clarinet's first three overtones would be 270 Hz, 450 Hz, and 630 Hz, respectively.