Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 79

With sound waves in a fluid such as air, the sound pressure at any point is the difference between the total pressure and normal atmospheric pressure. The sound pressure fluctuates with time and can be positive or negative with respect to the normal atmospheric pressure.

Sound varies in magnitude and frequency and it is normally convenient to give a single number measure of the sound by determining its time‐averaged value. The time average of the sound pressure at any point in space, over a sufficiently long time, is zero and is of no interest or use. The time average of the square of the sound pressure, known as the mean square pressure, however, is not zero. If the sound pressure at any instant t is p(t), then the mean square pressure, 〈p²(t)〉_t, is the time average of the square of the sound pressure over the time interval T:

(3.8)

where 〈〉_t denotes a time average.

It is usually convenient to use the square root of the mean square pressure:

which is known as the root mean square (rms) sound pressure. This result is true for all cases of continuous sound time histories including noise and pure tones. For the special case of a pure tone sound, which is simple harmonic in time, given by p = P cos(ωt), the rms sound pressure is

(3.9)

where P is the sound pressure amplitude.