Interference of two radio waves

[username12345]

Homework Statement

Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points along the line connecting the two sources.

At what distance from source A is there constructive interference between points A and B?

Homework Equations

Let P be the point of constructive interference:

$$r_1 - r_2 = m\lambda$$ where $$r_1$$ is the distance from A to P and $$r_2$$ is the distance from P to B.

These were the hints given, and don't make sense.

The Attempt at a Solution

I got the answer of 2.5 metres by drawing a diagram and estimating where the two waves would cross (constructive interference). The answer was correct, a lucky guess...

I don't know how to apply that equation. Does it need to be applied twice? For m I would use the value of 1?

 

[Redbelly98]

m could be any integer, not just 1.

Try m = 0 or 1, and see what you can come up using your equation,

r₁ - r₂ = m λ​

 

[nlightner]

I would approach this problem by first understanding the concept of constructive interference. When two waves meet, they can either interfere constructively (adding up to create a larger amplitude) or destructively (canceling each other out). In this case, the two waves are coherent, meaning they have the same frequency and are in phase with each other.

In order to determine the distance from source A where constructive interference occurs, we can use the equation r_1 - r_2 = m\lambda, where r_1 is the distance from source A to the point of constructive interference, r_2 is the distance from the point of constructive interference to source B, m is an integer representing the order of the interference, and \lambda is the wavelength of the waves.

Since we are only considering points along the line connecting the two sources, we can simplify the equation to r_1 = r_2. This means that the distance from source A to the point of constructive interference is equal to the distance from the point of constructive interference to source B.

Since the wavelength of the waves is given as 6.00 meters, we can substitute this value into the equation and solve for r_1:

r_1 = r_2 = m\lambda = 1(6.00m) = 6.00m

Therefore, the distance from source A where constructive interference occurs is 6.00 meters. This is consistent with our previous estimate of 2.5 meters, as the two sources are 5.00 meters apart and the point of constructive interference would be halfway between them.

In conclusion, by understanding the concept of constructive interference and using the given equation, we can determine the distance from source A where constructive interference occurs. This approach is more accurate and reliable than simply estimating the answer.