Please solve Phi 2. The 1st two are correct. Question 16 of 21 Incorrect Map Sap

Question

Please solve Phi 2. The 1st two are correct.

Question 16 of 21 Incorrect Map Sapling Learning Two traveling waves are generated on the same taut string.Individually, the two traveling waves can be described by the following two equations = (1.97 = (5.53 y,(xu) cm)sin|k,x+(0.243 rad / s)1+ ) cm)sink,K-(6.84 rad/s)t+ If both of the above traveling waves exist on the string at the same time, what is the maximum positive displacement that a point on the string can ever have displacent thav a point on the string can ever have at the same time, what is the maximum positive Number 7.5 cin What are the smallest positive values of the unknown phase constants (in radians) such that the above displacement occurs at the origin (x0) at time t 2.34 s? Number Number rad = | | 17.57 rad Previous Give Up & View Solution O Check Answer Next Exit Hint

Explanation / Answer

for maximum +ve positive dispalcement to occur.

y1 = 1.97 cm and y2 = 5.52 cm

hence,

sin(k1x + 0.243t + phi1) = 1

k1x + 0.243t + phi1 = (4n + 1) pi/2

n = 0, 1, 2

0 + (0.243 * 2.34) + phi1 = (4n + 1) pi/2

0.568 + phi1 = (4n + 1) pi/2

for n = 0

phi1 = 1 rad   

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And

sin(k2x - 6.84t + phi2) = 1

k2x - 6.84t + phi2 = (4n + 1) pi/2

n = 0, 1, 2   

16 + phi2 = (4n + 1) pi/2
for phi2 to be smallest we have to take negative values of angle then

hence 16 + phi2 = - (4n + 3) pi/2
n = 0,1,2,3,

for n = 0

phi2 = -3pi/2 + 16 = 11.29 rad

for n =1

phi2 = -7pi/2 + 16 = 5 rad s

for n= 2

phi2 = - 11pi/2 + 16 = -1.28 rad

so smallest +ve value is 5 rad. .......Ans

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