Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called sound. Most sound that people recognize as musical is dominated by periodic or regular vibrations rather than non-periodic ones; that is, musical sounds typically have a definite pitch). The transmission of these variations through air is via a sound wave. In a very simple case, the sound of a sine wave, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very pure tone. Pure tones can be produced by tuning forks or whistling. The rate at which the air pressure oscillates is the frequency of the tone, which is measured in oscillations per second, called hertz. Frequency is the primary determinant of the perceived pitch. Frequency of musical instruments can change with altitude due to changes in air pressure. Pressure (the symbol: p) is the ratio of force to the area over which that force is distributed. In other words, pressure is force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure (also spelled gage pressure)[a] is the pressure relative to the local atmospheric or ambient pressure. While pressure may be measured in any unit of force divided by any unit of area, the SI unit of pressure (the newton per square metre) is called the pascal (Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. A pressure o
1 Pa is small; it approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa). The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is: where: A, the amplitude, is the peak deviation of the function from zero. f, the ordinary frequency, is the number of oscillations (cycles) that occur each second of time. ? = 2?f, the angular frequency, is the rate of change of the function argument in units of radians per second ?, the phase, specifies (in radians) where in its cycle the oscillation is at t = 0. When ? is non-zero, the entire waveform appears to be shifted in time by the amount ?/? seconds. A negative value represents a delay, and a positive value represents an advance. Sine wave MENU0:00 5 seconds of a 220 Hz sine wave Problems listening to this file? See media help. The oscillation of an undamped spring-mass system around the equilibrium is a sine wave. The sine wave is important in physics because it retains its waveshape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.