Question

A system oscillates with a fundamental frequency of 100 Hz and higher modes of 150 Hz, 200 Hz, 250 Hz, 300 Hz, 350 Hz, and 400 Hz. How many harmonics are there?

a) 6
b) 5
c) 7
d) 8

Answer 1

Only four frequencies listed are harmonics of the fundamental frequency: the fundamental frequency itself (100 Hz) and whole number multiples of it, which are 200 Hz, 300 Hz, and 400 Hz. This results in a total of four harmonics.

Step-by-step explanation:

The question involves the concept of harmonics in a vibrating system. In such systems, the lowest resonant frequency is known as the fundamental frequency, and any higher resonant frequencies are termed overtones.

Each resonant frequency that is a whole number multiple of the fundamental frequency is considered a harmonic. The fundamental frequency itself is also referred to as the first harmonic.

In the given scenario, the system oscillates with a fundamental frequency of 100 Hz and has higher modes at 150 Hz, 200 Hz, 250 Hz, 300 Hz, 350 Hz, and 400 Hz.

Since harmonics are integer multiples of the fundamental frequency, the 150 Hz mode is not a harmonic of 100 Hz because 150 is not a whole number multiple of 100. Thus, the list of harmonics is: 100 Hz (first harmonic), 200 Hz (second harmonic), 300 Hz (third harmonic), and 400 Hz (fourth harmonic).

Therefore, the system has a total of four harmonics, including the fundamental frequency.