The Physics Underlying Harmony

Wave Basics 2: Anatomy

The Properties of a Wave 

   There are four basic parts to a wave: wavelength, amplitude, period, and frequency.

  • Wavelength (Fig 4) - Intuitively enough, this is the physical distance between two consecutive waves, measured from the crest of one wave to the crest of the next.  Humans can hear sound waves that have wavelengths of anywhere from a few centimeters up to several meters, meaning that the wave in Fig. 4 is actually audible.
  • Amplitude (Fig 4) - This is the 'height' of the wave, measured from the x-axis to the crest.  Since the wave is symmetrical across the x-axis, it is also the distance from the x-axis to the trough.  Since sound is actually longitudinal, this 'height' represents how compressed the air gets.  The amplitude determines the volume of a sound; higher amplitude means louder sound.  Amplitude is usually measured in decibels (dB).
  • Period (Fig 5) - Period is the amount of time it takes for 1 wavelength to pass by a specific point, measured in seconds.  Watch the red ball that's moving straight up and down in Figure 5.  Every time it peaks over a crest, it takes two seconds for it to reach the next crest, meaning that the period for this wave is 2 s.
  • Frequency (Fig 5) - Frequency is the number of waves that pass by a given point per second; it's simply the inverse of the period.  Since the wave in Figure 5 has a period of 2 seconds, it has a frequency of .5 wavelengths per second; the red ball travels half a wave per second.  We measure frequency in hertz (Hz) where 1 Hz = 1 wavelength / s. The frequency determines the pitch of a sound; a higher frequency (more waves per second) means a higher pitch.  Humans can hear anywhere from 20 Hz up to around 20,000 Hz.
 [static wave]
Fig 5: a static wave with parts labeled (UBC)


[animated image of a wave passing by a point]
Fig 6: wave moving past a fixed point (Weiderman)

Relating Them All

You've probably noticed that wavelength, period, and frequency are all closely related.  Frequency is simply 1 over the period, and so we can represent their relationship with equation 1.  For any given material and temperature, the speed of sound is the same - sound waves all travel the same speed (around 340 m/s in surface air at 20° C) regardless of their wavelength or amplitude (NASA).  This means that the only way to increase the amount of waves that pass by per second (frequency) is to shorten their wavelength, so that we can fit more waves in a given space; this relationship can be seen in equation 2.  Using these, we can also find the relationship between wavelength and period (equation 3). 

equation 1
[equation 1]
 equation 2
[eq 2]
 equation 3
[eq 3]

Sound Samples

Although a visual representation of amplitude and frequency are good, the true understand comes from being able to hear the different frequencies and amplitudes.  Below I have a collection of sine waves at three select frequencies and two amplitudes.  I've also include the wavelengths to give an idea of the physical lengths of the sounds you're hearing.


 Frequency: 150 Hz
Wavelength: around 2.3 m.
 Frequency: 300 Hz
Wavelength: around 1.1 m.
 Frequency: 1020 Hz
Wavelength: around 33 cm.
low amplitude:
high amplitude:

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