As I listened to a car honking its horn for a long period of time far away with no pause, I noticed that the quality of the sound changed subtly several times over the first second or two. I think this is a result of echoes: at first I heard only the incident horn, but after a short time it was joined by one, two, three, several echoes of the original horn. Depending on the particular details of the time delays, some of the harmonics in each echo interfered constructively with those in the original sound, while others interfered destructively.
Aside from what this implies about what we can learn about our built environment from analyzing the sound, it occurred to me as being a very easy effect to simulate; this took me about 15 minutes:
/* ./horn | aplay */
#include <stdio.h>
#include <stdint.h>
typedef uint8_t u8;
u8 wave(long long t)
{
return (t & 128 ? 256 - (t & 255) : 128 + (t & 127)) >> 1;
}
u8 horn(long long t)
{
enum { attack = 600 };
int v = t < 0 ? 0 : t > attack ? 256 : t * t * 256 / attack / attack;
return wave(t) * v >> 8;
}
int main()
{
for (int a = 0; a < 32000; a++) {
putchar(horn(a - 1000)
+ (horn(a - 6242) * 64 >> 8)
+ (horn(a - 8932) * 32 >> 8)
+ (horn(a - 12333) * 64 >> 8)
+ (horn(a - 3013) * 128 >> 8)
);
}
}
The waveform of the sound doesn’t sound very much like a horn, but the changes in the tonal quality over time are similar to what I was hearing.