Question

There are two coherent microwave sources in the x–y plane. These sources are emitting in phase at a wavelength of ????=1.78 cm. One of the sources, ????1, is located along the y ‑axis at y1, and the second source, ????2, is located at the point x2=3.74 cm, y2=13.4 cm. Assume y1>y2. If the phase difference at the origin between the two sources is ????=152∘, where is the first source located on the y ‑axis?

Answer 1

`y_1 = 14.65 cm`

Step-by-step explanation:

As we know the relation between phase difference and path difference

`\Delta \phi = (2\pi)/(\lambda)(\Delta x)`

so we will have

`\Delta \phi = 152^o`

`\Delta \phi = 0.84 \pi`

`(2\pi)/(1.78 cm)(\Delta x) = 0.84 \pi`

`\Delta x = 0.75 cm`

now distance of two sources are

`d_1 = √(x_2^2 + y_2^2)`

`d_1 = √(3.74^2 + 13.4^2)`

`d_1 = 13.9 cm`

Now we have

`y_1 - 13.9 = 0.75`

`y_1 = 14.65 cm`