K323 / 2027
General properties of waves overview

Topic 4 of 6

Sound, pitch and loudness

A vibrating source makes a disturbance in a material medium. In air, the disturbance travels as compressions and rarefactions.

Longitudinal motion is parallel to wave travel. Amplitude describes the size of an oscillation; frequency describes how often it repeats.

From a vibrating source to travelling sound

A tuning fork's prongs or a loudspeaker cone vibrate. As the source moves forwards, it pushes nearby air into a slightly smaller region. As it moves back, that region can become more spread out. Interactions between neighbouring regions pass the disturbance onwards.

  • A compression has greater local pressure and density than the undisturbed air.
  • A rarefaction has lower local pressure and density than the undisturbed air. It still contains particles; it is not a vacuum.

Sound in air is a travelling compression pattern

A vibrating speaker disturbs nearby air. The diagram shows a longitudinal model, with all distances and particle motions schematic.

A speaker produces compressions and rarefactions while air particles oscillate locallyA speaker at the left is the vibrating source; a short blue double arrow below it indicates its vibration. Rows of air-particle symbols show two crowded compression regions and a more spread-out rarefaction between them. The rarefaction still contains air particles. A green arrow shows the sound pattern travelling right. A blue horizontal double arrow below the orange marked particle shows the directions of its local oscillation, parallel to propagation. Adjacent compression centres are one wavelength apart. Particle rows are a simplified representation and not a solid lattice. The air does not stream from the speaker to a listener with the wave.Sound travels rightCompressionCompressionRarefactionParticle moves to and froSpeakerOne wavelength
The source's vibration creates travelling compressions and rarefactions. A marked air particle oscillates locally, parallel to the wave's travel. Adjacent compression centres are one wavelength apart; the particle does not travel from the speaker to the listener.

The repeated back-and-forth motion along the direction of travel makes sound in air longitudinal. Sound in water can be described by the same compression-and-rarefaction model. The medium carries the disturbance and energy while its particles oscillate about local positions.

Sound needs a medium

Sound can travel through gases, liquids and solids because their particles interact. It cannot propagate through an ideal vacuum, where there are no particles to pass on this mechanical disturbance.

Observation and explanation

A vibrating source in a bell jar

A sounding source is placed in a bell jar. As air is removed, it becomes much less audible outside even though the source can still be seen vibrating.

The reduced sound supports the need for a material transmission medium. The observation does not mean that vibration has stopped. In a real apparatus, solid supports and remaining gas can still transmit some sound, so the demonstration is not a perfect removal of every pathway.

Change amplitude and frequency separately

Under comparable conditions, a sound wave of greater amplitude is louder. A sound wave of greater frequency has a higher pitch. Increasing amplitude does not by itself require a higher frequency.

The following graphs represent the displacement of an air particle against time at the same observation position for three separate sounds. Their vertical units are micrometres (µm), where 1 µm = 0.000001 m, not microphone voltage.

Compare amplitude and period separately

These are air-particle displacement-time graphs at one observation point, with the same axis scales and comparable conditions. They are not paths through the air or microphone voltages.

A: reference sound

Sound A: amplitude 0.20 micrometres and period 4.0 millisecondsThe vertical axis is particle displacement in micrometres, with the same scale from minus 0.40 to plus 0.40 for all three graphs. The horizontal axis runs from zero to eight milliseconds on the same scale. This sound has amplitude 0.20 micrometres, period 4.0 milliseconds and frequency 250 hertz. It completes two cycles in eight milliseconds.Particle displacement / micrometres-0.4-0.20.0+0.2+0.402468Time / ms

Amplitude 0.20 micrometres; period 4.0 ms; frequency 250 Hz.

B: larger amplitude

Sound B: amplitude 0.40 micrometres and period 4.0 millisecondsThe vertical axis is particle displacement in micrometres, with the same scale from minus 0.40 to plus 0.40 for all three graphs. The horizontal axis runs from zero to eight milliseconds on the same scale. This sound has amplitude 0.40 micrometres, period 4.0 milliseconds and frequency 250 hertz. It has twice the displacement amplitude of A and the same frequency.Particle displacement / micrometres-0.4-0.20.0+0.2+0.402468Time / ms

Amplitude 0.40 micrometres; period 4.0 ms; frequency 250 Hz.

C: shorter period

Sound C: amplitude 0.20 micrometres and period 2.0 millisecondsThe vertical axis is particle displacement in micrometres, with the same scale from minus 0.40 to plus 0.40 for all three graphs. The horizontal axis runs from zero to eight milliseconds on the same scale. This sound has amplitude 0.20 micrometres, period 2.0 milliseconds and frequency 500 hertz. It completes four cycles in eight milliseconds, twice as many as A, so its frequency is double. Equal displacement amplitude at a different frequency does not establish equal perceived loudness.Particle displacement / micrometres-0.4-0.20.0+0.2+0.402468Time / ms

Amplitude 0.20 micrometres; period 2.0 ms; frequency 500 Hz.

B is louder than A under the comparable conditions and has the same pitch. C has a higher pitch than A; its unchanged displacement amplitude alone does not establish equal perceived loudness.

A and B have the same period but different amplitudes. C has a shorter period than A. These are particle-displacement traces, not curved paths along which air particles travel.
Sound A: 0.20 µm amplitude, 4.0 ms period
4.0 ms = 0.0040 s, so f = 1/0.0040 = 250 Hz.
Sound B: 0.40 µm amplitude, 4.0 ms period
Its frequency is also 250 Hz, so it has the same pitch as A. Its larger amplitude makes it louder under the stated comparable conditions. Doubling amplitude does not mean that perceived loudness is exactly doubled.
Sound C: 0.20 µm amplitude, 2.0 ms period
2.0 ms = 0.0020 s, so f = 500 Hz. Its higher frequency gives a higher pitch than A. Equal displacement amplitude at a different frequency does not establish an exact equality of perceived loudness.

Read a microphone trace with its own units

A microphone and recording system can display a sound signal against time. That display usually represents the microphone's electrical output, rather than air-particle displacement measured in metres. Use the labelled vertical quantity.

To compare signal amplitudes, keep the microphone, recording gain, source distance and relevant surroundings the same. A taller trace caused by turning up the recording gain is not evidence that the source became louder. The time between repeated equivalent peaks still gives the period when the time scale is known.

Amplitude and frequency answer different questions. Taller oscillations concern amplitude; more cycles in the same time concern frequency. Neither means that the air itself travels all the way from source to receiver.

Optional check At the same observation point in comparable conditions, sound B has twice the particle-displacement amplitude of sound A, but both have period 4.0 ms. How do they compare?
At the same observation point in comparable conditions, sound B has twice the particle-displacement amplitude of sound A, but both have period 4.0 ms. How do they compare?