Converting Propagation Distance to Delay Length

We may regard the delay-line memory itself as the fixed ``air'' which propagates sound samples at a fixed speed $c$ ($c=345$ meters per second at $22$ degrees Celsius and 1 atmosphere). The input signal $x(n)$ can be associated with a sound source, and the output signal $y(n)$ (see Fig.2.1 on page ) can be associated with the listening point. If the listening point is $d$ meters away from the source, then the delay line length $M$ needs to be

$$M = \frac{d}{cT} \quad{\hbox{samples}},$$

where $T$ denotes the discrete-time sampling interval. In other words, the number of samples delay is the propagation distance $d$ divided by $cT$ , the distance sound propagates in one sampling interval. In practice, rounding $M=d/cT$ to the nearest integer causes no audible difference, unless the echo time is so short that the system is not really perceived as an echo (we'll learn about ``comb filters'' in §2.6 below).