CHAPTER 16. THE PHYSICS OF MUSIC 16.5
fundamental frequency
higher frequencies
higher frequencies
resultant waveform
Figure 16.4: The qualityof a tone depends on itsmixture of harmonics.
The resultant waveformis very different from thefundamental frequency.Even though the two waves
have the same main frequency, they do not sound the same!
Chapter 16 — Summary
See the summary presentation ( Presentation: VPkzl at http://www.everythingscience.co.za)
- Instruments producesound because they formstanding waves in strings or pipes.
- The fundamental frequency of a string or a pipe is its natural frequency. The wavelength of the
fundamental frequencyis twice the length of thestring or pipe when bothends are fixed or
both ends are open. It isfour times the length ofthe pipe when one endis closed and one end
is open.
- When the string is fixed at both ends, or the pipe is open at both endsthe first harmonic is
formed when the standing wave forms one whole wavelength in the string or pipe. The second
harmonic is formed when the standing wave forms 1^12 wavelengths in the string or pipe.
- When a pipe is openat one end and closed at the other, the first harmonic is formed when the
standing wave forms^113 wavelengths in the pipe.
- The frequency of a wave can be calculated with the equation f =vλ.
- The wavelength of astanding wave in a stringfixed at both ends can be calculated using
λn=n^2 −L 1.
- The wavelength of astanding wave in a pipewith both ends open can be calculated using
λn=^2 nL.
