7.4.1 Waves

Acoustic analysis is based on the sine and cosine functions. Fig. 7.12 shows a plot of a sine wave, in particular the function:

$$ y=A*sin(2\pi ft) $$

where we have set the amplitude A to 1 and the frequency f to 10 cycles per second.

Recall from basic mathematics that two important characteristics of a wave are its frequency and amplitude. The frequency is the number of times a second that a wave repeats itself, i.e. the number of cycles. We usually measure frequency in cycles per second. The signal in Fig. 7.12 repeats itself 5 times in .5 seconds, hence 10 cycles per second. Cycles per second are usually called Hertz (shortened to Hz), so the frequency in Fig. 7.12 would be described as 10 Hz. The amplitude A of a sine wave is the maximum value on the Y axis.

The period T of the wave is defined as the time it takes for one cycle to complete, defined as

$$ T=\frac{1}{f} $$

In Fig. 7.12 we can see that each cycle lasts a tenth of a second, hence $ T = .1 $ seconds.