Question

Two radio antennas separated by d = 302 m as shown in the figure below simultaneously broadcast identical signals at the same wavelength. A car travels due north along a straight line at position x = 1330 m from the center point between the antennas, and its radio receives the signals. Note: Do not use the small-angle approximation in this problem.
(a) If the car is at the position of the second maximum after that at point O when it has traveled a distance y = 400 m northward, what is the wavelength of the signals?
[Incorrect: Your answer is incorrect.]
Return to the derivation of the locations of constructive interference in Young's double slit experiment. m

(b) How much farther must the car travel from this position to encounter the next minimum in reception?
[Incorrect: Your answer is incorrect.]
You must work with the full trigonometric expressions for constructive and destructive interference because the angles are not small. m

Answer 1

d = 302 m , x = 1330 m

(a) y = 400 m

m = 2

from pythogerous law

H = (1330^2+302^2)^0.5

H = 1363.86 m

sin(theta) = 400/1363.86

sin(theta) = 400/1363.86

theta = 17.05 degrees

tan (17.5) = 0.307

we are not using small angles

dsin(theta) = m*lamda

302*(400/1363.86) = 2*lamda

lamda = 44.3 m

(b)

dsin(theta) = (m+0.5)*lamda

302*Sin(theta) = (2+0.5)*44.3

sin(theta) = 0.366

theta = 21.47 degrees

tna(theta) = y'/x

tan(21.47) = y'/1330

y' =523 m

y' -y = 523 - 400 = 123 m