Question

As a first approximation, sound waves can be described using rays to express position, propagation direction, and propagation path. An equation describing echo can be defined as; y(n) = x(n) + Ža,x(n-de) k=1 where : x(n) represents the straight path signal a, is an attenuation factor between 0 and 1 for reflected signals d. is a time delay for reflected signals In this equation y(n) is the sound sink and the straight path ray from the sound source is represented by x(n). The summation represents any reflected rays that make it to the sink. The summation takes into account the energy loss due to reflection ak and the increase in time, or delay dk, taken to reach the sink. The scenario for three rays is shown in the figure 11. Here the source is the speaker and the sink is the microphone.

Answer 1

Solution: Object da microphone Speaker K X -- . et us denote the height of the object from the direct line connecting Speakers of microphone be 'h' and the distance (horisonzal) as well as from the speakers be d. Note that had given the position as well as Propagation direction from the ray pain. set the total distance from the speaker to the microphone be's

So, the line taken for the direct vay will be t h where c is speed of sound Time takın by ray reflected from the object will be Thus the time taken data-ti for delay is given an - Volt + VW0763 If we have a different plain the land h would be different and we would have a different delay for the there patern shos: The Echo equation can be written as y = a(46) + 9,0 = -0,)+ą,? (5e-dz) where a (4c) represents the stright signal a(2/2 - d.) + x ( - dz) represents the and of 3rd signals Their respective d, & da is a function of their dah Calculate above generally there would be characterigal waves in which ( -d) represents the plane of an represents their propagation. This implie, we could get an Incliface of sound at the місторици.