Sound and Music - Mission SM5 Detailed Help

The first harmonic frequency of a musical instrument is 200 Hz. The second, third, and fourth harmonic frequencies are ____ Hz, ____ Hz, and ____ Hz respectively.

Natural Frequencies and Harmonics:
Every object has a natural frequency or a set of natural frequencies at which it tends to vibrate at. When struck, plucked, strummed or somehow disturbed, the object will vibrate at one of the natural frequencies in its set of natural frequencies. These individual frequency values are often referred to as the harmonic frequencies of the string or air column. The lowest harmonic frequency is referred to as the fundamental frequency. The other frequency values in the set of natural frequencies are whole number multiples of the fundamental frequency value.

Each harmonic frequency in a set of natural frequencies is different than the previous harmonic in that its standing wave pattern has one additional antinode (and one additional node). The addition of an antinode makes the wavelength shorter and the frequency higher. The second harmonic has twice the number of antinodes as the first harmonic. The third harmonic has three times the number of antinodes as the first harmonic. The fourth harmonic has four times the number of antinodes as the first harmonic. The fifth harmonic has ... and so on. Thus, compared to the first harmonic, each higher harmonic has a frequency that is a whole number multiple of the first harmonic. This mathematical pattern is expressed by the equation stated in the Formula Frenzy section.

The nth harmonic frequency (fn) of a set of natural frequencies is ntimes the frequency of the fundamental or first harmonic frequency (f1).
fn= n •f1

where n is a whole number. The second harmonic frequency (f2) can be determined by substituting 2 into the above equation in place of n.