Pure tone

Sine wave is called an audible tone when the vibration generating it mathematically (except at its beginning and end) can be described by a sine or cosine function. Strictly speaking, this is a theoretical construct that still exists in its perfect form either in nature can be technically realized. "Natural " generated sounds, such as musical instruments, are not pure tones, because more and more natural frequencies of the vibrating body ( string, air column, etc. ) involved (see overtone ). The tuning fork as well as the organ pipe, stopped in very wide scale produce very obertonarme sounds that approximate to the pure sine wave.

In addition to applications of artificially produced sinusoidal tones mainly in the technical field, the concept of sine tone for spectral analysis is important. Sine tones are the building blocks of any sound event dar.

Mathematical Background

The vibration can be described by one at each time t, the instantaneous displacement y (t) describes the function. In a pure tone that vibration function has the form

The amplitude, f is the frequency of the oscillation. The deflection and the amplitude are distances ( lengths). One may also use various other variables which describe the instantaneous state of the vibrating body, such as the sound pressure or the particle velocity instead of the deflection. The amplitude is then in each case the maximum value assumed this size.

By means of Fourier analysis is any time-dependent signal as a sum of sinusoidal signals of different frequency and phase can be represented.

Technical production and application

Depending on which claims are made on the allowable distortion, the effort increases to generate a sine tone.

The sine wave is used for example in the calibration and measurement of frequency responses of sound technical equipment, but also in listening tests, or as a mixture of several pure tones in DTMF dialing.

Human perception

The sound of the sine wave is generally perceived as sterile or empty. He appears " whistling " because pipes ( flutes) are relatively poor in overtones.

The characteristic sound of a musical instrument is created as the sum of different sine tones (root, harmonics ) whose amplitudes and phases sometimes change during the sounding of the tone yet.

440Hz sine wave? / I