Ex-IIT ques(Waves)

is d ans 98 fr 2nd one??????????

can u post the answers ............. if my ans maches ill post soln.

at least posrt options aditya....

y1 + y2 is net disp of wave...................

acos(0.5pi x - 100pi t ) + acos(0.46pi x - 92 pi t)

2acos(96 pi t)cos(4 pi t) <--[edited calc error here]

y1 + y2 = 0 if and only if one of the angles are of form (2n+1)pi/2 ... n E N

96pi t = (2n+1)pi/2

192 t = 2n + 1

t = (2n + 1) /(384)
= n/96 + 1/192

let it be in interval 0-1 ....

191/192 = n/96

191/2 = n

[191/2] = 95 times....................

4 t = (2n+1)/2

t = n/4 + 1/8 .........................

[7/2] = 3

98 it is sorry for that trivial mistake

correct if rong ..........

no ................

u forgot how to convert two trigo functions to product form !!

@ iit comin
acos(0.5pi x - 100pi t ) + acos(0.46pi x - 92 pi t)

at x =0

acos(100pi t ) + acos(92 pi t)

2acos(192 pi t)cos(8 pi t) /// error

and for maxima ... put n pi

shud be satisfy both the cos functions simultaneously ,,,,

oh... its 192/2 , 8/2 inside the cos sorry .....see post 6 for corrected soln.

Thanks ram, iitimcomin and riddle.