Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A . Con

step 1 This is chapter 35 problem number four. We have two antennas A and B. The distance between them

Two radio antennas A and B radiate in phase. Antenna B is...

Two radio antennas $A$ and $B$ radiate in phase. Antenna $B$ is $120 \mathrm{~m}$ to the right of antenna $A .$ Consider point $Q$ along the extension of the line connecting the antennas, a horizontal distance of $40 \mathrm{~m}$ to the right of antenna $B .$ The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point $Q ?$ (b) What is the longest wavelength for which there will be constructive interference at point $Q ?$

Two radio antennas $A$ and $B$ radiate in phase. Antenna $B$ is $120 \mathrm{~m}$ to the right of antenna $A .$ Consider point $Q$ along the extension of the line connecting the antennas, a horizontal distance of $40 \mathrm{~m}$ to the right of antenna $B .$ The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point $Q ?$
(b) What is the longest wavelength for which there will be constructive interference at point $Q ?$

Key Concepts

Frequency-Wavelength Relationship

The frequency-wavelength relationship is a fundamental property of waves, where the speed of a wave (such as light or radio waves) is equal to the product of its frequency and wavelength. Adjusting one of these parameters while keeping the wave speed constant directly affects the other. This relationship is essential for understanding how variations in frequency impact the interference pattern, including the positions of constructive and destructive interference.

Phase Difference

Phase difference is the measure of the separation between the phases of two or more waves at a given point in space. It is determined by the relative timing and the path difference of the waves. The phase difference directly influences whether interference will be constructive or destructive, as well as the resulting intensity of the combined wave.

Path Difference

Path difference refers to the difference in distances that two waves travel from their respective sources to a particular point. This difference is crucial in determining whether the waves will interfere constructively or destructively. Depending on the path difference, the waves may arrive either in phase or out of phase, significantly affecting the interference outcome.

Constructive Interference

Constructive interference occurs when waves meet in phase, meaning their crests and troughs align, resulting in reinforcement of amplitude. The condition for constructive interference is typically that the path difference between the waves is an integer multiple of the wavelength, causing them to add together and produce a stronger signal.

Wave Interference

Wave interference is the phenomenon that occurs when two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude. The way in which these waves add depends on their relative phases and amplitudes, leading to observable patterns such as areas of increased intensity (constructive interference) or decreased intensity (destructive interference).

Destructive Interference

Destructive interference happens when waves meet out of phase, such that the crest of one wave aligns with the trough of another. This phase misalignment causes the waves to cancel each other out partially or completely, and typically the path difference is an odd multiple of half the wavelength, leading to a reduction or nullification of the wave amplitude at the point of interest.

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