An effect similar to multi-path in acoustics is echoing or reverberation. To see the effects of an echo in an acoustic signal consider the simulation of echoes on the handel.matsignal y[n]. Pretend that this piece is being played in a round theater where the orchestra is in the middle of two concentric circles and the walls on one half side are at a radial distances of 17 meters (corresponding to the inner circle), and 34 meters (corresponding to the outer circle) on the other side (yes, an unusual theater!) from the orchestra. The speed of sound is 345 meters/s. Assume that the recorded signal is the sum of the original signal y[n], and attenuated echoes from the two walls so that the recorded signal is given by

r[n] = y[n] + 0.8y[n − N₁] + 0.6y[n − N₂]

where N₁ is the delay caused by the closest wall and N₂ the delay caused by the farther wall. The recorder is at the center of the auditorium where the orchestra is and we record for 10 s.

(a) Find the values of the two delays N₁ and N₂(remember these are integers). The sampling frequency F_s of handel is given when you load it in.

(b) Simulate the echo signal. Plot r[n]. Use sound to listen to the original and the echoed signals.