Simple Acoustic Theory

    What is sound?

     Sound is created when something vibrates setting up small fluctuations in air pressure. These fluctuations, if they are steady and regular, will be perceived as tones when they hit the ear drum and pass though the aural chain to the brain.

    An important feature of these vibrations is their frequency, ie the number of times per second that the object vibrates. A whole vibratory cycle consists of the thing, say a string, moving from rest, all the way in one direction back though the rest point, all the way in the other direction and back to where it started. That is one cycle. When the number of cycles rises to over 20 cycles per second, the human ear may well hear it. A cycle per second is usually referred to as a Hertz (Hz) after the German physicist Heinrich Hertz.

    A young person with good hearing can hear sounds from about 20Hz to about 18,000Hz. With age, that sensitivity declines. Loud industrial sounds, rock music played loudly etc can damage hearing.

    Lower frequencies (slower) are perceived as bass notes, while high frequencies sound high. When a sound occurs at a single steady frequency, we hear it as a note. The pitch of the note is the brain's way of interpreting the frequency of the vibrations. Fortunately the brain is rather good at differentiating between notes of different pitches. We can hear differences of less than one percent. Hearing is more sensitive in the range 2000Hz to 5000Hz. These sounds seem louder than those at the outer range of hearing.

    We are sensitive to particular ratios in frequencies. For example if one note is twice the frequency of another, we say it has a pitch one octave higher. If the frequency is doubled again, the note goes up another octave. So the series f, 2f, 4f, 8f etc is a series of notes rising by an octave each time.

    A note consisting of just one frequency is called a pure tone and does not occur often when musical instruments produce tones. A tuning fork or electronic device may produce pure tones. Most instruments however produce notes which are more complex. Within one note there is a blend of frequencies present. The nature of the blend determines what we hear and how we describe that tone.

    Look at three examples of sounds:


    1. If there is no recurring pattern to the frequencies present, ie no one frequency dominates, then we hear the sound as a flurry of vibrations, or noise. eg maracas.

    2. If there is only one steady frequency present, we have a pure tone. eg tuning fork, some flutes

    3. If there is a single sound with several frequencies present, we can usually hear a plurality of frequencies but we assign a pitch to the dominant one. Strings fit that description. When we hear a blend of frequencies we assign a tonal description to the sound. If there are lots of high frequencies present we say the sound is bright. If there are fewer high frequencies present we say the sound is more mellow, rounded, smoother etc.

    In a sound with multiple frequencies present, the different frequencies are called partials. The lowest is called the fundamental and that is the one we usually identify as the pitch of the note. Above the fundamental frequency are the overtones. Overtones can be harmonic or inharmonic. If they are harmonic then they are some integral multiple of the fundamental frequency, ie f, 2f, 3f, 4f, 5f etc. Sometimes that is called the harmonic series, or just the harmonics. Harmonic overtones tend to blend well whilst inharmonic overtones give an edge to the tone.

    The timbre of a sound will depend on the mix of overtone frequencies. If the overtones are all exact multiples of the fundamental, they will complete their wave patterns at the same time as the fundamental and hence reinforce the sound. You would probably say that the sound is coherent, full and easily recognised in pitch. Some overtones will be more prominent than others though and that will affect the timbre. Also the overtones may be slightly sharp due to the physical properties of the instrument making the tone. For example thick strings usually produce upper partials which are very slightly sharp. The longer and more flexible a string is, the purer will be the set of overtones. That is why a huge grand piano is usually preferred to a small upright by concert pianists.

    A sound may be perceived as quite low in pitch even when the fundamental doesn't have a lot of energy. This can happen when the soundboard is small for example. The pattern of overtones is present however and the brain can discern that pattern of overtones and reconstruct the fundamental, even though it may be very weak. The brain determines that the fundamental should be there in that series, so you imagine you hear the low note. Low notes on dulcimers often display that characteristic.

    © Gillian Alcock 1998
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