Question

If a wind instrument, such as a tuba, has a fundamental frequency of 32.0 Hz, what are its first three overtones? It is closed at one end. (The overtones of a real tuba are more complex than this example because it is a tapered tube.)

a) 96.0 Hz, 160.0 Hz, 224.0 Hz
b) 32.0 Hz, 64.0 Hz, 96.0 Hz
c) 64.0 Hz, 128.0 Hz, 192.0 Hz
d) 32.0 Hz, 96.0 Hz, 160.0 Hz

Answer 1

For a tuba that is closed at one end with a fundamental frequency of 32.0 Hz, the first three overtones are odd multiples of the fundamental frequency: 96.0 Hz, 160.0 Hz, and 224.0 Hz.

Step-by-step explanation:

To determine the first three overtones of a wind instrument like a tuba with a fundamental frequency of 32.0 Hz that is closed at one end, we need to recognize the pattern of frequencies that such a tuba can produce. For a tube that is closed at one end, the resonant frequencies are odd multiples of the fundamental frequency. Therefore, the first overtone will be 3 times the fundamental, the second is 5 times, and the third is 7 times the fundamental frequency.

So for the tuba with a fundamental frequency of 32.0 Hz, the first three overtones would be:

1. First overtone: 32.0 Hz × 3 = 96.0 Hz
2. Second overtone: 32.0 Hz × 5 = 160.0 Hz
3. Third overtone: 32.0 Hz × 7 = 224.0 Hz

Therefore, the correct answer is (a) 96.0 Hz, 160.0 Hz, 224.0 Hz.