Two radio antennas separated by d=290 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 positionx = 1,400 m from the center point between the antennas, and its radio receives the signals. Hint: 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 of y = 400 m northward, what is the wavelength of the signals?XYour response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digitaccuracy to minimize roundoff error. m(b) How much farther must the car travel to encounter the next minimum in reception?XYour response differs from the correct answer by more than 10%. Double check your calculations. m

Answered: Two radio antennas separated by d = 290…

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Two radio antennas separated by d
=
290 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 = 1,400 m from the center point between the antennas, and its radio receives the signals. Hint: 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 of y = 400 m northward, what is the wavelength of the signals?
X
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit
accuracy to minimize roundoff error. m
(b) How much farther must the car travel to encounter the next minimum in reception?
X
Your response differs from the correct answer by more than 10%. Double check your calculations. m

Expert Solution

Step 1: Interference maximum between sources

The condition for a second maximum in the interference pattern is given by:

$d space sin space left parenthesis theta right parenthesis equals m lambda$

Where:
$d$ is the distance between the two sources (two antennas).
$theta$ is the angle from the centerline to the location of the maximum.
$m$ is the order of the interference pattern.
$lambda$ is the wavelength.

The condition for a minimum in the interference pattern is given by:

$d space sin space left parenthesis theta right parenthesis equals left parenthesis m plus 1 half right parenthesis lambda$

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