How do you calculate the frequency of the nth harmonic?

The frequency of the nth harmonic is calculated by multiplying the fundamental frequency by the harmonic number (n).

In more detail, the fundamental frequency, also known as the first harmonic, is the lowest frequency of a periodic waveform. In music, it's the pitch of the note. In physics, it's the lowest resonance frequency of a vibrating object. The nth harmonic, on the other hand, is a whole number multiple of this fundamental frequency.

To calculate the frequency of the nth harmonic, you simply multiply the fundamental frequency by the harmonic number. For example, if the fundamental frequency is 50 Hz, the frequency of the second harmonic (n=2) would be 2*50 = 100 Hz, the third harmonic (n=3) would be 3*50 = 150 Hz, and so on.

This principle is based on the physics of waves and vibrations. When an object vibrates or a wave oscillates, it does so at certain frequencies, which we call resonant frequencies. The fundamental frequency is the lowest of these, and each harmonic is a higher resonant frequency. These harmonics form a series, with each one being a whole number multiple of the fundamental frequency.

This concept is crucial in many areas of physics and engineering, including acoustics, telecommunications, and signal processing. It's also fundamental to the theory of music, where the harmonics of a note form the basis of its timbre or tone colour. Understanding how to calculate and work with harmonics is therefore a key skill in these fields.

Remember, the frequency of the nth harmonic is simply the fundamental frequency times the harmonic number. This simple formula allows you to calculate the frequency of any harmonic, given the fundamental frequency.