in the figure a rario transmitting station operating at a frequency of 100 MHz has two identical coherent antennas. Antenna A is 124 m from point P and anternna B is 421 m from point P. what type of interference, destructive, constructive, or neither occurs in point P.

Question

in the figure a rario transmitting station operating at a frequency of 100 MHz has two identical coherent antennas. Antenna A is 124 m from point P and anternna B is 421 m from point P. what type of interference, destructive, constructive, or neither occurs in point P.

so the answer is saying it is constructive but i keep getting destructive. can someone help me out?

i know that with the given frequency we can find the wavelength.
so the speed of light/ frequency = 3E8/100E6 HZ

so the wavelength ends up being = 3.
Now we subtract 421m - 124 m = 297 m.
297m / 3 = 99 and i'm saying its destructive because it is odd. someone please help me out :(

Answer 1

the difference in distance to the two antennas is a WHOLE NUMBER of wavelengths

... this means that waves arrive in phase ... constructive interference

Answer 2

I understand your confusion. Let's break down the problem and calculate the phase difference between the waves received at point P from each antenna to determine whether constructive or destructive interference occurs.

The formula to calculate the phase difference is:

Δφ = (2π / λ) * Δd

Where:
Δφ is the phase difference
λ is the wavelength
Δd is the difference in path lengths

First, we have the frequency given, which is 100 MHz. To find the wavelength, we use the equation:

λ = (speed of light) / (frequency)

λ = 3 × 10^8 m/s / 100 × 10^6 Hz
λ = 3 meters

Now, we calculate the path length difference, Δd, between the two antennas:

Δd = |dA - dB| = |124 m - 421 m| = 297 m

Using the calculated values, we can find the phase difference:

Δφ = (2π / 3) * 297 m
Δφ ≈ 624.78 radians

To determine interference type, we need to analyze the phase difference. In general, constructive interference occurs when the phase difference is a multiple of 2π, and destructive interference occurs when the phase difference is an odd multiple of π.

In this case, Δφ is approximately 624.78 radians, which is neither a multiple of 2π nor an odd multiple of π. Therefore, the interference between the two waves at point P is neither completely constructive nor completely destructive.

It's important to note that the answer may vary slightly depending on the precision of your calculations, but the main conclusion remains the same.