Sound and vibration

Source, medium and listener

A plucked string moves around its resting position. Through the instrument's bridge and body, this movement disturbs the surrounding air. Regions of compression and rarefaction travel outward, while individual air particles move locally. The air beside the string does not have to travel across the room to carry the sound to your ear. Energy is passed through the medium.

A useful listening diagram therefore has three parts: source, path and receiver. Changing the source can change the sound itself; moving a listener changes the path; changing a microphone changes what is captured. If a recorded instrument sounds different from the one beside you, inspect all three parts. The difference is not necessarily evidence that the instrument was played differently.

References: [1]

How fast, how large and how far apart?

Frequency counts repetitions per second and is measured in hertz, or Hz. Amplitude describes the size of an oscillation, such as the pressure variation at a location. Wavelength is the distance between corresponding points in successive cycles. These answer different questions. A taller waveform on an audio display is not automatically a higher note; the horizontal spacing of its repeating pattern matters for frequency.

For a wave travelling at speed v, the relation is v = f × λ: speed equals frequency multiplied by wavelength. In the same air conditions, increasing the frequency shortens the wavelength. This does not mean that high notes rush past low notes. For ordinary sound propagation in air, their speeds are effectively the same. The original calculation below uses 340 metres per second as a convenient approximate value.

References: [1]

Resonance gives vibration a musical setting

An instrument has preferred ways of vibrating. A string fixed at both ends can support standing-wave patterns with stationary points, called nodes. The simplest pattern has one broad vibrating segment; higher patterns divide the string into more segments. For an ideal flexible string these patterns have frequencies related by whole-number multiples. Real materials introduce departures from that ideal model.

Pluck an unplugged electric guitar and then an acoustic guitar. The strings may produce similar pitches, but their bodies and methods of radiating sound differ. A string by itself moves relatively little air. Coupling it to a larger vibrating surface changes how effectively its energy reaches the room. The instrument is a connected system: excitation, vibration, transfer and radiation all contribute to the audible result.

References: [2]

What a waveform can and cannot show

An audio waveform plots changing signal amplitude against time. Zoomed out, it can reveal attacks, pauses and broad changes in level. Zoomed in, a nearly repeating pattern may help you estimate a period. A spectrum answers a different question by displaying how energy is distributed across frequencies. Neither display is a complete description of musical meaning, and neither substitutes for listening.

Try recording one soft pluck and one firmer pluck while keeping the microphone still. Compare the beginning and the decay rather than only the tallest peak. A harder attack may alter the mixture of frequencies as well as the signal level. If the recorder automatically adjusts gain, its display can hide part of the difference. Note the recording conditions before drawing conclusions from a picture.

References: [2]

What to remember

• The disturbance travels while particles move locally.
• Frequency, amplitude and wavelength describe different properties.
• Resonance and sound radiation help explain instrument behaviour.