Waves & Sound

A travelling pattern is not a travelling parcel of air

A mechanical wave needs a medium, such as air, water or a solid. In an ideal sound wave in air, local pressure and particle motion vary as the disturbance propagates. Air particles oscillate around local positions; they do not have to travel all the way from the source to the listener for the sound to arrive.

Sound in air is commonly modelled as a longitudinal wave: particle motion is along the direction in which the disturbance travels. A transverse-wave sketch has motion across that direction. A drawn sine curve can represent sound pressure plotted against position or time; it does not mean that air follows a visible up-and-down snake through the room.

Worked example: turn counts into a wavelength

Use an invented measurement of 20 complete cycles in 0.10 seconds. Frequency is cycles divided by elapsed time: 20/0.10 = 200 hertz. The period is time per cycle, 0.10/20 = 0.005 seconds. The two numbers describe the same repetition in reciprocal ways.

Assume a sound speed of 340 metres per second for this model. Wavelength is speed divided by frequency, so 340/200 = 1.7 metres. At 400 hertz with the same assumed speed, the wavelength is 0.85 metres. Doubling frequency halves wavelength here. That result depends on holding wave speed fixed; it is not a claim that sound travels at the same speed in every medium or condition.

Amplitude is a different variable

Amplitude describes the size of the variation being modelled, such as pressure variation for sound. Raising amplitude does not, by itself, double the number of cycles per second. Pitch is strongly related to frequency, while perceived loudness and timbre involve further features and the listener’s context. Avoid using louder and higher as interchangeable explanations.

A photograph of an instrument shows a possible vibrating source, not the pressure pattern around it. Similarly, the invented values above demonstrate a calculation, not an actual measurement of the pictured guitar. A complete record would state what was measured, which units were used and what conditions the speed assumption represents.

Read the axes before interpreting a wave drawing

A pressure-versus-time graph at one point reveals repetition over time. A pressure-versus-distance graph at one moment reveals spacing across distance. Their horizontal axes answer different questions. Label the axis before counting cycles or measuring a wavelength. You can compare two annotated paper patterns and do the calculations without producing sound, testing your hearing or using recording equipment.