The voice of the echo across distance
How long an echo takes and how loud it returns at 30 and at 100 braccia
Two proportion problems about echoes. If an echo answers in 2 beats over 30 braccia, in how long will it answer one that is 100 braccia distant? And if over 30 braccia it returns in 2 beats with 2 degrees of loudness, in how many degrees of loudness will it show itself at 100 braccia? A diagram at the top lays out the distances with points b, c, d, e, f, g and a, marked 30 and 100.
On this page
Time an echo takes at 30 versus 100 braccia
Leonardo asks how the return time of an echo scales with distance: if the voice answers in 2 beats at 30 braccia, in what time will it answer at 100 braccia? The question treats the echo's delay as proportional to the space it must travel.
How the loudness of an echo falls with distance
A companion problem sets the echo's strength as a proportion: if at 30 braccia it returns in 2 beats with 2 degrees of loudness, in how many degrees of loudness will it appear at 100 braccia? Leonardo seeks the rule relating perceived loudness to distance.
Diagram of the echo distances
A line diagram at the top of the sheet lays out the successive positions with points b, c, d, e, f, g converging on a, the spans marked 30 and 100. It fixes the geometry underlying the two echo questions.