Question

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example because its double reed makes it act more like a tube closed at one end.)

a) 180.0 Hz, 270.0 Hz, 360.0 Hz
b) 90.0 Hz, 180.0 Hz, 270.0 Hz
c) 270.0 Hz, 360.0 Hz, 450.0 Hz
d) 90.0 Hz, 270.0 Hz, 450.0 Hz

Answer 1

The first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz and is open at both ends are 180.0 Hz, 270.0 Hz, and 360.0 Hz. The correct answer is a) 180.0 Hz, 270.0 Hz, 360.0 Hz.

Step-by-step explanation:

The first three overtones of a bassoon with a fundamental frequency of 90.0 Hz, which is open at both ends, are based on the harmonic series of a pipe open at both ends. Such a pipe supports all harmonics, which are integer multiples of the fundamental frequency.

The first harmonic (or fundamental frequency) is 90.0 Hz. Therefore, the first overtone, which is the second harmonic, has a frequency of 2 × 90.0 Hz = 180.0 Hz.

The second overtone is the third harmonic and will be 3 × 90.0 Hz = 270.0 Hz. The third overtone is the fourth harmonic, which equates to 4 × 90.0 Hz = 360.0 Hz. Hence, the correct sequence for the first three overtones is 180.0 Hz, 270.0 Hz, and 360.0 Hz.