Assignment:
The question is the example on page 2 of the attachment (entitled 'Uniform Transducer'). it states that the center of the finger is at z'=L/4. I assume this is an arbitrary position. For Eq (2.4.6), the contribution from the left-hand finger is added. I'm not entirely sure how this equation is arrived at. It does not look like a mere addition.
The contributions from the other fingers are added to give Eq(2.4.7). Whilst I understand where the first line in (2.4.7) comes from (although unsure where lambda appeared from), I do not understand at all how the second line of (2.4.7) is arrived at from the integral given on the previous line. I understand that the Double Angle Formula is used to get line 3 of (2.4.7).
Eq(2.4.8) perplexes me: if N is large then kl (zero response) ~ 2*pi.... which we know equals +/-2N. I'm missing something here.
Finally, how is Eq (2.4.9) and Eq (2.4.10) arrived at?
Attachment:- Delta function model of transducer.rar