**Transcription for Educational Website:**---**Problem Overview:**Two radio antennas are separated by a distance $ d = 290 $ meters, as depicted in the figure. These antennas broadcast identical signals with the same wavelength simultaneously. A car moves directly north along a straight path at a position $ x = 1,400 $ meters from the center point between the antennas. The car's radio receives the signals.**Important Note:** Do not use the small-angle approximation in this problem.---**Diagram Explanation:**The diagram shows:- Two antennas on the left, marked with the distance $ d $ between them.- A car moving along a vertical path northward from point $ O $, where $ O $ is the midpoint between the antennas.- The path is indicated by the vertical axis labeled $ y $.- The horizontal axis is labeled $ x $, showing the car's distance from the center point.---**Questions:****(a)** If the car is at the position of the second maximum after point $ O $ when it has traveled a distance of $ y = 400 $ meters northward, what is the wavelength of the signals?- **Answer Box:** [Input required]- **Feedback:** "Your response is within 10% of the correct value. This may be due to roundoff error, or you may have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error."**(b)** How much farther must the car travel to encounter the next minimum in reception? - **Answer Box:** [Input required]- **Feedback:** "Your response differs from the correct answer by more than 10%. Double-check your calculations."---**Instructions:** Use precise calculations and ensure the values are accurate to minimize errors.

Answered: Two radio antennas separated by d = 290…

College Physics

11th Edition

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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**Transcription for Educational Website:**

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**Problem Overview:**

Two radio antennas are separated by a distance $ d = 290 $ meters, as depicted in the figure. These antennas broadcast identical signals with the same wavelength simultaneously. A car moves directly north along a straight path at a position $ x = 1,400 $ meters from the center point between the antennas. The car's radio receives the signals.

**Important Note:** Do not use the small-angle approximation in this problem.

---

**Diagram Explanation:**

The diagram shows:
- Two antennas on the left, marked with the distance $ d $ between them.
- A car moving along a vertical path northward from point $ O $, where $ O $ is the midpoint between the antennas.
- The path is indicated by the vertical axis labeled $ y $.
- The horizontal axis is labeled $ x $, showing the car's distance from the center point.

---

**Questions:**

**(a)** If the car is at the position of the second maximum after point $ O $ when it has traveled a distance of $ y = 400 $ meters northward, what is the wavelength of the signals?
- **Answer Box:** [Input required]
- **Feedback:** "Your response is within 10% of the correct value. This may be due to roundoff error, or you may have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error."

**(b)** How much farther must the car travel to encounter the next minimum in reception?
- **Answer Box:** [Input required]
- **Feedback:** "Your response differs from the correct answer by more than 10%. Double-check your calculations."

---

**Instructions:** Use precise calculations and ensure the values are accurate to minimize errors.

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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